Equilibrium constant. Real constant Equilibrium constant dependence
K p = ∏ p i ν i (\displaystyle K_(p)=\prod p_(i)^((\nu )_(i)))
For example, for the oxidation reaction of carbon monoxide:
2CO + O 2 \u003d 2CO 2
the equilibrium constant can be calculated from the equation:
K p = p C O 2 2 p C O 2 ⋅ p O 2 (\displaystyle K_(p)=(\frac (p_(CO_(2))^(2))(p_(CO)^(2)\cdot p_ (O_(2))))) K p = K x P Δ n (\displaystyle K_(p)=K_(x)P^(\Delta n))where Δn- change in the number of moles of substances during the reaction. It's clear that K x depends on pressure. If the number of moles of reaction products is equal to the number of moles of starting materials ( Δ n = 0 (\displaystyle \Delta n=0)), then K p = K x (\displaystyle K_(p)=K_(x)).
Standard equilibrium constant
The standard equilibrium constant of a reaction in a mixture of ideal gases (when the initial partial pressures of the reaction participants are equal to their values in the standard state = 0.1013 MPa or 1 atm) can be calculated by the expression:
K 0 = ∏ (p i ~) v i (\displaystyle K^(0)=\prod ((\tilde (p_(i))))^(v_(i))) where p i ~ (\displaystyle (\tilde (p_(i))))- relative partial pressures of the components, p i ~= p i / p i 0 (\displaystyle (\tilde (p_(i)))=p_(i)/p_(i)^(0)).The standard equilibrium constant is a dimensionless quantity. She is associated with Kp ratio:
K p = K 0 (p i 0) Δ n (\displaystyle K_(p)=K^(0)(p_(i)^(0))^(\Delta n))It is seen that if p i 0 (\displaystyle p_(i)^(0)) expressed in atmospheres (p i 0) Δ n = 1 (\displaystyle (p_(i)^(0))^(\Delta n)=1) and K p = K 0 (\displaystyle K_(p)=K^(0)).
For a reaction in a mixture of real gases in the standard initial state, the partial fugacity of gases is taken equal to their partial pressures f i 0 = p i 0 (\displaystyle f_(i)^(0)=p_(i)^(0))= 0.1013 MPa or 1 atm. Kf associated with K0 ratio:
K f = K 0 (γ i p i 0) Δ n (\displaystyle K_(f)=K^(0)(\gamma _(i)p_(i)^(0))^(\Delta n)) where γ i- coefficient of fugacity of the i-th real gas in the mixture.Equilibrium constant for reactions in heterogeneous systems
FeO t + CO g = Fe t + CO 2gthe equilibrium constant (assuming that the gas phase is ideal) has the form:
K p = p C O 2 p C O (\displaystyle K_(p)=(\frac (p_(CO_(2)))(p_(CO))))Thermodynamic description of equilibrium
Along with the designation Q for the ratio of the activities of substances at an arbitrary moment of the reaction t ("coefficient reaction")
Q r = ( S t ) σ ( T t ) τ ( A t ) α ( B t ) β = ∏ a j (t) ν j ∏ a i (t) ν i = ∏ a n (t) ν n (\displaystyle Q_ (r)=(\frac (\left\(S_(t)\right\)^(\sigma )\left\(T_(t)\right\)^(\tau ))(\left\(A_( t)\right\)^(\alpha )\left\(B_(t)\right\)^(\beta )))=(\frac (\prod a_(j(t))^(\nu _( j)))(\prod a_(i(t))^(\nu _(i))))=\prod a_(n(t))^(\nu _(n)))(notation for the reaction below; the last equality is written in the notation that the stoichiometric coefficients are taken with a "+" sign for products and with a "-" sign for starting materials)in chemical thermodynamics, the notation is used K eq for the same form of the relationship between the equilibrium activities of substances
K e q = [ S ] σ [ T ] τ [ A ] α [ B ] β = ∏ a j (t = ∞) ν j ∏ a i (t = ∞) ν i = ∏ a n (t = ∞) ν n (\ displaystyle K_(eq)=(\frac ([S]^(\sigma )[T]^(\tau ))([A]^(\alpha )[B]^(\beta )))=(\frac (\prod a_(j(t=\infty))^(\nu _(j)))(\prod a_(i(t=\infty))^(\nu _(i))))=\prod a_(n(t=\infty))^(\nu _(n)))(that is, the ratio of activities at the moment t = ∞ (\displaystyle t=\infty ), at the moment of equilibrium). The following is a thermodynamic description of chemical equilibrium and a description of the relationship K eq with the standard Gibbs energy of the process.In a system where a chemical reaction is taking place
α A + β B ⇌ σ S + τ T (\displaystyle \alpha A+\beta B\rightleftharpoons \sigma S+\tau T)equilibrium can be described by the condition
(d G d ξ) T , p = 0 (\displaystyle \left((\frac (dG)(d\xi ))\right)_(T,p)=0) where ξ (\displaystyle \xi ) there is a chemical variableor, the same equilibrium condition can be written using chemical potentials as
α μ A + β μ B = σ μ S + τ μ T (\displaystyle \alpha \mu _(A)+\beta \mu _(B)=\sigma \mu _(S)+\tau \mu _ (T))where are the chemical potentials
μ A = μ A ⊖ + R T ln ( A ) (\displaystyle \mu _(A)=\mu _(A)^(\ominus )+RT\ln\(A\)) here (A) - strictly speaking, the activity of the reagent A; under assumptions about ideal gases, they can be replaced by pressures, for real gases, they can be replaced by fugacity, under the assumption that the solution obeys Henry's law, can be replaced by mole fractions, and under the assumption that the solution obeys Raoult's law, by partial pressures; for a system in equilibrium, it can be replaced by the equilibrium molar concentration or by the equilibrium activity. Δ r G o = − R T ln K e q (\displaystyle \Delta _(r)G^(o)=-RT\ln K_(eq))The equilibrium composition of the mixture and the direction of the reaction
The above "reaction coefficient" Q(other designations found in the literature - Ω (\displaystyle \Omega ) or π (\displaystyle \pi ), "reaction product")
Q r = ∏ a n (t) ν n (\displaystyle Q_(r)=\prod a_(n(t))^(\nu _(n)))reflects the ratio of the current activities of all participants in the reaction and can be used to determine the direction of the reaction at the moment for which Q is known
If at the moment t the coefficient Q > K, then the current activities of the products are greater than the equilibrium ones, and therefore they must decrease by the moment when the equilibrium is established, that is, at the moment the reverse reaction is taking place; If Q = K, then the equilibrium state has been reached and the rates of the forward and reverse reactions are equal; If Q< K, то v 1 > v − 1 (\displaystyle v_(1)>v_(-1))
Using the value Q r (\displaystyle Q_(r)) the equation is written chemical reaction isotherms
Δ G p , T = R T ln Q r − R T ln K e q = R T ln Q r K e q = ∑ ν i μ i (\displaystyle \Delta G_(p,T)=RT\ln Q_(r) -RT\ln K_(eq)=RT\ln (\frac (Q_(r))(K_(eq)))=\sum \nu _(i)\mu _(i))Where ν (\displaystyle \nu )- stoichiometric coefficients (for products - with the "+" sign, for starting materials - with the "-" sign; the same as in the expressions for Q and K), and µ (\displaystyle \mu ) are the chemical potentials and the standard Gibbs energy and the standard constant are
Δ G p , T o = − R T ln K e q o = ∑ ν i μ i o (\displaystyle \Delta G_(p,T)^(o)=-RT\ln K_(eq)^(o)=\sum \nu _(i)\mu _(i)^(o))Where μ o (\displaystyle \mu ^(o))- standard chemical potentials
The isotherm equation shows how the value of Q is related to the change in the free energy of the reaction:
At Q > K (\displaystyle Q>K) for direct reaction ∆ G > 0 (\displaystyle \Delta G>0), that is ∑ ν j μ j (\displaystyle \sum \nu _(j)\mu _(j)) for products of the direct reaction more than for the starting substances - this means that the direct reaction is prohibited (which means that the reverse is not prohibited); at Q = K (\displaystyle Q=K) for direct reaction ∆ G = 0 (\displaystyle \Delta G=0), that is, the reaction has reached an equilibrium state; at Q<
K
{\displaystyle Q
The value, by definition, makes sense only for the state of equilibrium, that is, for the state with v 1 v − 1 = 1 (\displaystyle (\frac (v_(1))(v_(-1)))=1) and ∆ G r = 0 (\displaystyle \Delta G_(r)=0). Value K e q (\displaystyle K_(eq)) says nothing about reaction rates, but it describes the composition of the system at equilibrium.
If K >> 1, then products of the (direct) reaction predominate in the system. If K<< 1, то в системе преобладают исходные вещества (продукты обратной реакции)
Standard States
The standard Gibbs energy of a reaction in a gas mixture is the Gibbs energy of a reaction at standard partial pressures of all components equal to 0.1013 MPa (1 atm). The standard Gibbs energy of a reaction in solution is the Gibbs energy at the standard state of the solution, which is taken as hypothetical a solution with the properties of an extremely dilute solution, but with the concentration of all reagents equal to one. For a pure substance and liquid, the standard Gibbs energy is the same as the Gibbs energy of formation of these substances. The value of the standard Gibbs energy of the reaction can be used for an approximate assessment of the thermodynamic possibility of the reaction proceeding in a given direction, if the initial conditions do not differ greatly from the standard ones. In addition, by comparing the values of the standard Gibbs energy of several reactions, one can choose the most preferable ones, for which it has the highest modulo negative size.
Kinetic description
For a reversible chemical reaction, the equilibrium constant K eq can be expressed in terms of the rate constants of the forward and reverse reactions. Consider an elementary reversible first-order chemical reaction
A ⇄ B (\displaystyle \mathrm (A) \rightleftarrows \mathrm (B) )By definition, equilibrium is given by the condition v 1 = v − 1 (\displaystyle v_(1)=v_(-1)), that is, the equality of the rates of the forward and reverse reactions.
According to the law of mass action v = k ∏ a j n j (\displaystyle v=k(\prod )(a_(j))^(n_(j)))
Where k is the rate constant of the corresponding reaction, and a j n j (\displaystyle (a_(j))^(n_(j))) are the equilibrium activities of the reactants of this reaction raised to powers equal to their stoichiometric coefficients
we can write the equilibrium condition in the form
1 = v 1 v − 1 = k 1 ∏ a A n A k − 1 ∏ a B n B (\displaystyle 1=(\frac (v_(1))(v_(-1)))=(\frac ( k_(1)(\prod )(a_(A))^(n_(A)))(k_(-1)(\prod )(a_(B))^(n_(B))))) 1 = k 1 k − 1 ⋅ ∏ a A n A ∏ a B n B = k 1 k − 1 ⋅ (K e q) − 1 (\displaystyle 1=(\frac (k_(1))(k_(-1 )))\cdot (\frac (\prod (a_(A))^(n_(A)))(\prod (a_(B))^(n_(B))))=(\frac (k_( 1))(k_(-1)))\cdot \left(K_(eq)\right)^(-1))(see thermodynamic description of the equilibrium constant), which is possible only if
K e q = k 1 k − 1 (\displaystyle K_(eq)=(\frac (k_(1))(k_(-1))))This important relationship provides one of the "points of contact" between chemical kinetics and chemical thermodynamics.
Multiple equilibria
In the case when several equilibria are established in the system at once (that is, several processes proceed simultaneously or sequentially), each of them can be characterized by its own equilibrium constant, from which it is possible to express the general equilibrium constant for the entire set of processes. We can consider such a situation using the example of the stepwise dissociation of dibasic acid H 2 A. Its aqueous solution will contain particles (solvated) H + , H 2 A, HA - and A 2- . The dissociation process proceeds in two stages:
H 2 A ⇌ H A − + H + : K 1 = [ H A − ] [ H + ] [ H 2 A ] (\displaystyle H_(2)A\rightleftharpoons HA^(-)+H^(+):K_( 1)=(\frac()())) H A − ⇌ A 2 − + H + : K 2 = [ A 2 − ] [ H + ] [ H A − ] (\displaystyle HA^(-)\rightleftharpoons A^(2-)+H^(+):K_ (2)=(\frac()()))K 1 and K 2 - constants of the first and second stages of dissociation, respectively. From them, you can express the "total" equilibrium constant, for the process of complete dissociation:
H 2 A ⇌ A 2 − + 2 H + : K 1 + 2 = [ A 2 − ] [ H + ] 2 [ H 2 A ] = K 1 K 2 (\displaystyle H_(2)A\rightleftharpoons A^( 2-)+2H^(+):K_(1+2)=(\frac (^(2))())=K_(1)K_(2))Another example of multiple equilibrium is the analysis of the precipitate/soluble complex compound system. Suppose there is an equilibrium
A g I 2 − (a q) ⇌ A g I (s o l i d) + I − (a q) (\displaystyle AgI_(2)^(-)(aq)\rightleftharpoons AgI(solid)+I^(-)(aq) )The reaction can be represented as two successive equilibria - the equilibrium of the decomposition of a complex ion into its constituent ions, which is characterized by an "instability constant" (the reciprocal of the "stability constant" β):
A g I 2 − (a q) ⇌ A g + (a q) + 2 I − (a q) : K 1 = α A g + α I − 2 α A g I 2 − = β − 1 (\displaystyle AgI_(2 )^(-)(aq)\rightleftharpoons Ag^(+)(aq)+2I^(-)(aq):K_(1)=(\frac (\alpha _(Ag^(+))\alpha _ (I^(-))^(2))(\alpha _(AgI_(2)^(-))))=\beta ^(-1))and equilibrium of the transition of ions from the volume of the solvent to the crystal lattice
A g + (a q) + I − (a q) ⇌ A g I (s o l i d) : K 2 = α A g I α A g + α I − (\displaystyle Ag^(+)(aq)+I^(- )(aq)\rightleftharpoons AgI(solid):K_(2)=(\frac (\alpha _(AgI))(\alpha _(Ag^(+))\alpha _(I^(-)))) )taking into account the fact that for solid substances the activity is assumed to be equal to 1 , and in dilute solutions activities can be replaced by molar concentrations, we get
K 2 = α A g I α A g + α I − = 1 [ A g + ] [ I − ] = 1 K s p (\displaystyle K_(2)=(\frac (\alpha _(AgI))(\ alpha _(Ag^(+))\alpha _(I^(-))))=(\frac (1)())=(\frac (1)(K_(sp))))where K sp (\displaystyle K_(sp))- solubility product
Then the total equilibrium will be described by the constant
A g I 2 − (a q) ⇌ A g I (s o l i d) + I − (a q) : K = α A g I α I − α A g I 2 − = K 1 ⋅ K 2 = 1 β ⋅ K s p ( \displaystyle AgI_(2)^(-)(aq)\rightleftharpoons AgI(solid)+I^(-)(aq):K=(\frac (\alpha _(AgI)\alpha _(I^(-) ))(\alpha _(AgI_(2)^(-))))=K_(1)\cdot K_(2)=(\frac (1)(\beta \cdot K_(sp))))And the value of this constant will be the condition for the predominance of a complex compound or a solid salt in an equilibrium mixture: as above, if K<< 1, то в равновесной смеси большая часть ионов связана в комплексное соединение, если K >> 1, then in the equilibrium state in the system, most of the ions are bound in the crystalline phase. reaction proceeding, respectively, at constant pressure or at constant volume. If a ∆ H > 0 (\displaystyle \Delta H>0)(the thermal effect is positive, the reaction is endothermic), then the temperature coefficient of the equilibrium constant d ln K p d T (\displaystyle (\frac (d\ln K_(p))(dT))) is also positive, that is, with increasing temperature, the equilibrium constant of the endothermic reaction increases, the equilibrium shifts to the right (which is quite consistent with the Le Chatelier principle).
Methods for calculating the equilibrium constant
Calculation methods for determining the equilibrium constant of a reaction usually come down to calculating in one way or another the standard change in the Gibbs energy during the reaction ( ∆G0) and then using the formula:
Δ G 0 = − R T ln K 0 (\displaystyle \Delta G^(0)=-RT\ln K^(0)), where R (\displaystyle R)- universal gas constant .At the same time, it should be remembered that the Gibbs energy is a function of the state of the system, that is, it does not depend on the path of the process, on the reaction mechanism, but is determined only by the initial and final states of the system. Therefore, if a direct definition or calculation ∆G0 for some reaction are difficult for some reason, you can choose such intermediate reactions for which ∆G0 is known or can be easily determined, and the summation of which will give the reaction in question (see Hess' Law). In particular, reactions of the formation of compounds from elements are often used as such intermediate reactions.
Entropy calculation of the change in the Gibbs energy and the equilibrium constant of the reaction
Entropy calculation method ΔG reactions is one of the most common and convenient. It is based on the ratio:
Δ G T = Δ H T − T Δ S T (\displaystyle \Delta G_(T)=\Delta H_(T)-T\Delta S_(T))or, respectively, for standard Gibbs energy changes:
Δ G T 0 = Δ H T 0 − T Δ S T 0 (\displaystyle \Delta G_(T)^(0)=\Delta H_(T)^(0)-T\Delta S_(T)^(0))Here ∆H0 at constant pressure and temperature is equal to the thermal effect of the reaction, the methods of calculation and experimental determination of which are known - see, for example, the Kirchhoff equation:
Δ H T 0 = Δ H 298 0 + ∫ 298 T Δ C p d T (\displaystyle \Delta H_(T)^(0)=\Delta H_(298)^(0)+\int _(298)^(T )\Delta C_(p)dT)It is necessary to obtain the change in entropy during the reaction. This problem can be solved in several ways, for example:
- According to thermal data - based on the Nernst thermal theorem and using information about the temperature dependence of the heat capacity of the reaction participants. For example, for substances that are in a solid state under normal conditions:
So, if known ∆ H 298 0 (\displaystyle \Delta H_(298)^(0)), Δ S 298 0 (\displaystyle \Delta S_(298)^(0)) and temperature dependences of heat capacity, ∆ G T 0 (\displaystyle \Delta G_(T)^(0)) can be calculated using the formula:
∆ G T 0 = ∆ H 298 0 − T ∆ S 298 0 + ∫ 298 T )^(0)-T\Delta S_(298)^(0)+\int _(298)^(T)\Delta C_(p)dT-T\int _(298)^(T)\Delta C_ (p)(\frac (dT)(T)))A somewhat simplified version of this formula is obtained by assuming the sum of heat capacities of substances to be independent of temperature and equal to the sum of heat capacities at 298 K:
Δ G T 0 = Δ H 298 0 − T Δ S 298 0 + Δ C p 298 (T − 298) − T ln T 298 (\displaystyle \Delta G_(T)^(0)=\Delta H_(298) ^(0)-T\Delta S_(298)^(0)+\Delta C_(p~298)(T-298)-T\ln (\frac (T)(298)))And an even more simplified calculation is carried out by equating the sum of heat capacities to zero:
Δ G T 0 = Δ H 298 0 − T Δ S 298 0 (\displaystyle \Delta G_(T)^(0)=\Delta H_(298)^(0)-T\Delta S_(298)^(0) )Transfer from ∆ G T 0 (\displaystyle \Delta G_(T)^(0)) to the equilibrium constant is carried out according to the above formula.
Under the influence of an external influence, the chemical equilibrium, being dynamic, shifts. According to the Le Chatelier principle, an increase in temperature shifts the chemical equilibrium towards an endothermic process.
Temperature also has an effect on the equilibrium constant. The study of the influence of temperature on chemical equilibrium is one of the main problems of thermodynamics.
The effect of temperature on the equilibrium constant follows from the dependence DG 0 = f(Т) 0 , which is described by the Gibbs-Helmholtz equation:
and which for standard conditions will look like:
(6.185)
Let's use the isotherm equation under standard conditions:
DG 0 = - RT lnK p (6.178)
Differentiate the isotherm equation with respect to temperature at Р = const
(6.186)
We substitute the values of DG 0 into the Gibbs-Helmholtz equation (15) and obtain the equation:
(6.187)
After the transformation, we obtain the equation of the Vant isobar -
Goffa: 
(6.188)
Similarly, the isochore equation can be derived:
(6.189)
If the systems are real gases, liquids or solids, then the equations (6.188, 6.189) will include K f and K a, which are expressed in terms of the fugacity and activity of the reactants.
Since K p does not depend on pressure, the partial derivative in equations (18, 19) can be replaced by a full one:
(6.190) 
(6.191)
(6.192) 
(6.193)
Expressions 6.190 and 6.191 are the Van't-Hoff isobar equations, and expressions 6.192 and 6.193 are the Van't-Hoff isochore equations in differential form.
Let us dwell on the consideration of the isobar equation (6.190).
It establishes a connection between the change in the equilibrium constant with temperature and the thermal effect of the reaction.
As can be seen from equation (6.190), the sign of the derivative depends on the sign of the heat of reaction DH 0, which leads to the following conclusions:
1. If the reaction in the forward direction proceeds with the release of heat (exothermic), i.e. DH< 0, то < 0. Это означает, что с ростом температуры константа равновесия К р уменьшается, следовательно, уменьшается выход продуктов, что возможно при смещении химического равновесия в сторону обратной реакции, т.е. в сторону эндотермического эффекта.
2. If the reaction in the forward direction proceeds with the absorption of heat (endothermic), i.e. DH > 0, then > 0.
This means that with increasing temperature, the equilibrium constant K p increases, therefore, the yield of products increases, the equilibrium shifts in the forward direction, i.e. also towards the endothermic effect. Thus, with an increase in temperature, in all cases, the equilibrium shifts towards heat absorption, which is consistent with the well-known Le-Chatelier principle.
3. If the reaction proceeds without absorption and release of heat, i.e. DH \u003d 0, then \u003d 0. This means that with a change in temperature, the equilibrium constant does not change, therefore, the equilibrium does not shift.
Therefore, it is obvious that the smaller the DH of the reaction, the weaker the effect of temperature on the equilibrium constant and on the equilibrium shift.
Thus, the direction of equilibrium shift as a result of temperature change is determined by the sign of the thermal effect, and the degree of equilibrium shift is determined by the magnitude of the thermal effect.
To carry out quantitative calculations of the dependence of the equilibrium constant K p on temperature, it is necessary to integrate the isobar equation, dividing the variables first
(6.194)
If the process is carried out at a temperature different from standard conditions, i.e. DH 0 \u003d DH 0 T, then the heat effect of the reaction is determined by the Kirchhoff equation:
(6.195)
If DH 0 changes relatively little with temperature, you can use the average value of the heat of reaction () for the temperature interval (T 1 - T 2) corresponding to the integration limits and consider it a constant value:
= 
(6.196)
This assumption is valid for a small temperature range or in the case when the heat capacity of the system changes insignificantly during the reaction.
After integrating equation (6.194), the isobar equation is obtained in integral form:
(6.197)
Using this equation, you can calculate the equilibrium constant at any temperature, if the value of the constant is known at some other temperature and the value for a given temperature interval is known. Often the temperature T 1 is taken equal to 298 K. In this case, if T 2 is not very different from T \u003d 298 K, or the value of DC p is relatively small, then we can take =. The value can, as is known, be determined using the standard heats of formation of the reaction participants according to the well-known consequence from the Hess law:
|
At T = 298 K it is easy to determine Kp(298) . To do this, it is necessary to determine the reactions using the standard isobaric potentials of the formation of the participants in the reaction, and then using the formula (6.178)
calculate K p(298) .
If, when integrating the isobar equation, instead of a definite integral, we take an indefinite one, then we get:
(6.199)
From this equation (25) it follows that ln K p depends linearly on the reciprocal of the absolute temperature, and the tangent of the slope of the straight line (Ðb) is equal to:
(6.200)
Let's do an analysis.
a) If the reaction is endothermic, i.e. if DN > 0, tgb< 0
Рb > 90 (Fig. 6.19, a)
b) If the reaction is exothermic, i.e. if DH< 0, tgb > 0
Ðb< 90 (рис. 6.19,б)
 |
Rice. 6.19. The dependence of the equilibrium constant of the reaction on T
A graph built in the coordinates lnK - can be used for graphical calculation of K p and if the value of K p at several temperatures is known. For more accurate calculations, and also in cases where the heat of reaction depends markedly on temperature and the temperature interval is large, when integrating the isobar equation, it is necessary to take into account the dependence of the heat effect on temperature.
To find this dependence, we integrate the Kirchhoff equation in the range from T 1 \u003d 0 to T 2 \u003d T, taking into account that
DC p \u003d Da + DvT + DST 2 + DC / T -2 (6.201)
(combined equation DC p for organic and inorganic compounds).
After integrating the Kirchhoff equation, we get:
(6.202)
DH \u003d DH 0 + DaT + 1 / 2DvT 2 + 1 / 3DST 3 - DC / T -1, (6.203)
where DH 0 is the constant of integration and is the heat of reaction at 0 K.
Substituting the resulting equation DH \u003d f (T) (6.203) into equation (6.194) and integrating in the range from T 1 \u003d 0 to T 2 \u003d T we get:
where I is the integration constant.
Obviously, in order to calculate K p according to equation (6.204), it is necessary to determine the values of DH 0 and the integration constant - I.
To determine I, you need to know K p at any one temperature, for example T \u003d 298 K. Substituting this value of K p (298) into equation (6.204), you can calculate the constant I, which is constant for this reaction. Then, knowing DH 0 and I for a given reaction, one can calculate K p at any temperature.
A quantitative characteristic showing the direction of the reaction and the shift in the concentration of substances is called the equilibrium constant of a chemical reaction. The equilibrium constant depends on the temperature and the nature of the reactants.
Reversible and irreversible reactions
All reactions can be divided into two types:
- reversible, simultaneously flowing in two mutually opposite directions;
- irreversible flowing in the same direction with the total consumption of at least one initial substance.
In irreversible reactions, insoluble substances are usually formed in the form of a precipitate or gas. These reactions include:
- combustion:
C 2 H 5 OH + 3O 2 → 2CO 2 + H 2 O;
- decomposition:
2KMnO 4 → K 2 MnO 4 + MnO 2 + H 2 O;
- connection with the formation of a precipitate or gas:
BaCl 2 + Na 2 SO 4 → BaSO 4 ↓ + 2NaCl.
Rice. 1. Precipitation of BaSO 4 .
Reversible reactions are possible only under certain constant conditions. The original substances give a new substance, which immediately breaks down into its constituent parts and is collected again. For example, as a result of the reaction 2NO + O 2 ↔ 2NO 2 nitric oxide (IV) easily decomposes into nitric oxide (II) and oxygen.
Equilibrium
After a certain time, the rate of the reversible reaction slows down. Chemical equilibrium is achieved - a state in which there is no change in the concentration of the starting substances and reaction products over time, since the rates of the forward and reverse reactions are equalized. Equilibrium is possible only in homogeneous systems, that is, all reacting substances are either liquids or gases.
Consider the chemical equilibrium on the example of the reaction of the interaction of hydrogen with iodine:
- direct reaction -
H 2 + I 2 ↔ 2HI;
- back reaction -
2HI ↔ H 2 + I 2 .
As soon as two reagents are mixed - hydrogen and iodine - hydrogen iodine does not yet exist, since simple substances only react. A large number of starting substances actively react with each other, so the rate of the direct reaction will be maximum. In this case, the reverse reaction does not proceed, and its rate is zero.
The rate of a direct reaction can be expressed graphically:
ν pr = k pr ∙ ∙ ,
where k pr is the rate constant of the direct reaction.
Over time, the reagents are consumed, their concentration decreases. Accordingly, the rate of the forward reaction decreases. At the same time, the concentration of a new substance, hydrogen iodide, increases. When accumulated, it begins to decompose, and the rate of the reverse reaction increases. It can be expressed as
ν arr = k arr ∙ 2 .
Hydrogen iodide is squared, since the coefficient of the molecule is two.
At some point, the rates of the forward and reverse reactions equalize. There is a state of chemical equilibrium.
Rice. 2. Graph of reaction rate versus time.
The equilibrium can be shifted either towards the starting materials or towards the products of the reaction. The displacement under the influence of external factors is called Le Chatelier's principle. Equilibrium is affected by temperature, pressure, concentration of one of the substances.
Constant calculation
In a state of equilibrium, both reactions proceed, but at the same time, the concentrations of substances are in equilibrium (equilibrium concentrations are formed), since the rates are balanced (ν pr \u003d ν arr).
Chemical equilibrium is characterized by the chemical equilibrium constant, which is expressed by the summary formula:
K p \u003d k pr / k arr \u003d const.
The reaction rate constants can be expressed in terms of the reaction rate ratio. Let's take the conditional equation of the reverse reaction:
aA + bB ↔ cC + dD.
Then the rates of the forward and reverse reactions will be equal:
- ν inc = k inc ∙ [A] p a ∙ [B] p b
- ν arr = k arr ∙ [C] p c ∙ [D] p d .
Accordingly, if
ν pr \u003d ν arr,
k ex ∙ [A] p a ∙ [B] p b = k arr ∙ [C] p c ∙ [D] p d .
From here we can express the ratio of constants:
k arr / k inc = [C] p c ∙ [D] p d / [A] p a ∙ [B] p b .
This ratio is equal to the equilibrium constant:
K p = [C] p c ∙ [D] p d / [A] p a ∙ [B] p b .
Rice. 3. The formula for the equilibrium constant.
The value shows how many times the rate of the forward reaction is greater than the rate of the reverse reaction.
What have we learned?
Reactions depending on the final products are classified into reversible and irreversible. Reversible reactions proceed in both directions: the starting materials form final products, which decompose into starting substances. During a reaction, the rates of the forward and reverse reactions are balanced. This state is called chemical equilibrium. It can be expressed as the ratio of the product of the equilibrium concentrations of the reaction products to the product of the equilibrium concentrations of the starting materials.
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Equilibrium constant
For a chemical reversible reaction, presented in general form:
aA+bB ^dD+eE,
it was found that, regardless of what the initial concentrations of the reagents were, whether or not the reaction products were present, the ratio remains constant in the state of equilibrium: where [A] /; , [AT] ; „ [D] ; „ [E]; , - equilibrium molar concentrations of reactants and reaction products; a, b, d, e - stoichiometric coefficients in the reaction equation; K c - chemical equilibrium constant.
The chemical equilibrium constant depends on the temperature, the nature of the substances, but does not depend on the concentration of the reacting substances, because it shows at what ratios of the products of the concentrations of reacting substances in the system chemical equilibrium occurs.
This formula is an expression of the law of mass action for equilibrium established by Guldberg and Waage (1867).
For equilibria between gaseous substances, it is more convenient to use not molar concentrations, but partial pressures of gaseous substances; in this case, the equilibrium constant is denoted by K p ("ka-er"):
D E R a pb A B
The equilibrium constant, expressed in terms of concentrations, and the equilibrium constant, expressed in terms of partial pressures of substances, are related by the relation:
K p \u003d K c RTAn,
where An is the difference between the coefficients in the formulas of gaseous substances in the right and left parts of the equation.
At Dp=0, the equilibrium constants K p and K c are equal.
Thus, the chemical equilibrium constant is a fraction, the numerator of which is the product of equilibrium concentrations (if the reaction proceeds in solution) or equilibrium partial pressures (for reactions in the gas phase) of the reaction products raised to powers whose exponents are equal to stoichiometric coefficients. And in the denominator - the product of the concentrations (or partial pressures) of the starting substances raised to the appropriate powers.
If a heterogeneous reaction occurs
2C(X) + 0 2 ^ 2CO,
then the equilibrium constant has the form
those. the expression for the equilibrium constant of a heterogeneous reaction includes the equilibrium concentrations of substances that are only in the liquid or gaseous phases.
The equilibrium constant determines the completeness of the reaction by the time the equilibrium state is reached: the greater the value of the equilibrium constant, the more the reaction products predominate in the equilibrium reaction mixture, the greater the yield of the reaction products.
Shift in chemical equilibrium. Le Chatelier's principle
When the conditions in which the system is located (temperature, pressure, concentration) change, the chemical equilibrium is disturbed. After some time, a new chemical equilibrium is established in the system, corresponding to new conditions. The transition from one equilibrium state to another is called a shift or displacement of equilibrium.
The direction of the shift of chemical equilibrium as a result of changes in external conditions is determined by the Jle Chatelier principle: if a system in true equilibrium is acted upon from the outside, changing any of the conditions that determine the position of equilibrium, then the system will increase one of the directions of the process, which weakens the effect of this impact, and the equilibrium position will shift in the same direction.
Briefly, this principle is formulated as follows: if a system in equilibrium is subjected to an external influence, then the equilibrium is shifted in such a direction that contributes to the weakening of this influence.
concentration constant
When calculating equilibria in real systems, it is necessary to take into account the presence of foreign substances and their influence on the behavior of the initial substances and products of the reaction under study. This effect can be expressed both in the electrostatic interaction of ions and in chemical interaction with the formation of slightly dissociated or poorly soluble products. In both cases, a shift in the equilibrium of the reaction under study is observed. The concentration constant is expressed in terms of total concentrations, and not the activities of the starting materials and reaction products. In the case when foreign substances do not enter into competing chemical reactions, the concentration constant can be expressed in terms of equilibrium concentrations. For convenience of study, the concentration constant expressed in terms of equilibrium concentrations is often called the real constant, and the concentration constant expressed in terms of total concentrations is called the conditional constant.
The state of equilibrium is characterized by a real (concentration) constant
if the differences from ideality are due only to electrostatic interactions A, B, C and D with foreign ions.
The activity and equilibrium concentration of any ion are functionally related to each other by a simple relationship. For example, for ion A
a A = γ A [A]
Proportionality factor γ , called the activity coefficient, characterizes the degree of deviation of the system from the ideal due to the electrostatic interactions of the ions involved in the reaction under study with foreign (or own, if their concentration is high) ions. In an ideal system a A = [A] and the activity coefficient is equal to one. This means that there are no electrostatic interactions.
The value of the activity coefficient depends on the charge and ionic strength created by all ions in the solution:
Here I- ionic strength; [i] is the equilibrium concentration of the ion; z i- its charge.
The activity coefficients of individual ions can be theoretically estimated using the Debye-Hückel formulas
If a I< 0.01 (1-3)
If a I< 0.1 (1-4)
Here BUT and AT - constants depending on the temperature and dielectric constant of the solvent (for water at 20°С A = 0.5 and B = 0.3); a - distance of maximum approach of ions; these values are usually given in reference tables. Since fluctuations in the values of a do not affect the final result too much, it is recommended to take a constant value a = 3 A. Therefore,
The activity coefficient of an individual ion cannot be measured experimentally, since it is impossible to obtain a solution containing only positive or only negative ions.
For the A m B n electrolyte, only the average activity coefficient can be experimentally determined, which is related to the activity coefficients of individual ions γ A and γ B by the relations:
for binary electrolyte AB
for electrolyte type A m B n
The average activity coefficient can also be calculated theoretically using the Debye-Hückel formulas
If a I< 0.01
If a I< 0.1
Here a, a and b have the same meanings as in formulas (1-3) and (1-4), therefore
At low ionic strengths (I< 0.1) величины средних коэффициентов активности, рассчитанные по формулам Дебая - Хюккеля и найденные экспериментально, удовлетворительно совпадают. Это говорит о правомочности использования в этих условиях формул (1-3) - (1-4) для расчета величин γ ± и активности электролитов. Эти же формулы используются и для расчета коэффициентов активности индивидуальных ионов, хотя правильность таких расчетов нельзя проверить экспериментально.
For a more accurate calculation of the activity coefficients, it is proposed to introduce additional terms into the Debye-Hückel formulas. For example, the Davis equation makes it possible to calculate the activity coefficients of electrolytes and individual ions for ionic strengths of 0.2 - 0.5 with an error not exceeding 10%. The Davis equation for the activity coefficient of an individual ion has the form:
and for the average activity coefficient of the electrolyte A m B n:
The values of the activity coefficients of individual ions at different ionic strengths and the average activity coefficients for electrolyte solutions of different concentrations, calculated using the Debye-Hückel formulas, are given in reference books.
Knowing the activity coefficients, one can estimate the activity of an ion or electrolyte in a solution. To facilitate the calculations, the following assumptions can be used:
1. The activity coefficients of ions of the same charge, regardless of the radius of the ions, are approximately equal. Therefore, reference books sometimes give average values of the activity coefficients for one-, two-, three-, and four-charged ions.
2. The activity coefficients of neutral particles in dilute electrolyte solutions are assumed to be equal to one.
3. Very dilute electrolyte solutions, such as a saturated solution of a sparingly soluble electrolyte, can be considered ideal.
Often, when calculating complex equilibria, the activity coefficients are taken equal to unity. This assumption is justified for a number of reasons. First, the values of the activity coefficients found using the Debye-Hückel formulas may in these cases turn out to be very far from the true ones. Secondly, the influence of chemical factors on equilibrium is much greater than that of electrostatic forces, so neglecting the latter when calculating complex equilibria does not introduce a noticeable error into the results.
