Estimate the value of the equilibrium constant at 655 K for each reaction in Problem 70. ( ΔHf^

Estimate the value of the equilibrium constant at 655 K for...

Key Concepts

Van’t Hoff Equation

The Van’t Hoff equation relates the change in the equilibrium constant of a reaction to the temperature and the standard enthalpy change of the reaction. This equation is essential for estimating the equilibrium constant at different temperatures and provides a linear relationship (when using logarithms) that helps interpret how energy changes within a reaction influence its equilibrium state.

Standard Enthalpy Change (?H°)

Standard enthalpy change is the heat absorbed or released during a reaction under standard conditions. It plays a critical role in determining the temperature dependence of the equilibrium constant, as indicated by the Van’t Hoff equation, by quantifying the energy difference between reactants and products and thus influencing the spontaneity and extent of the reaction.

Equilibrium Constant (K)

The equilibrium constant is a numerical value that expresses the ratio of the concentrations (or partial pressures) of products to reactants at equilibrium for a given chemical reaction. It provides insight into the extent of a reaction, indicating whether the formation of products or reactants is favored under specific conditions.

Temperature Dependence of Equilibrium

The equilibrium constant is sensitive to temperature changes as the relative amounts of reactants and products adjust with changing thermal energy. Understanding this dependence is crucial because, according to Le Chatelier’s principle and thermodynamic relationships, shifts in temperature can lead to changes in the equilibrium position, thereby altering the value of K.

Transcript

00:01 In this question we've been asked to determine the equilibrium constant k.

00:05 And since we are dealing with state functions, thermodynamic state functions, we can use the expression, standard, energy change is equal to negative r2, lin, k.

00:19 And this is our equilibrium constant that we are looking for.

00:23 So making k is subject to formula, we get k being equal to the exponent of negative, standard gives energy change divided by r -18.

00:31 So the main goal here in the first part of the question is to just determine this standard gives energy change.

00:38 And we know this to be standard gives energy change can be calculated from the standard enthalpy change minus t multiplied by the standard entropy change.

00:50 So since we are dealing with state functions, for example, for these two, we can use this expression to say, for example the standard enthalpy change is equal to the sum of the enthalpy changes of formation of the reactants of the products minus the sum of standard enthalpy change of formation of the reactants and we always have to make sure that we multiply by the respective stoichiometric coefficients because these expressions or these parameters are always given in per mole of substance so we always have to make sure that we always have to make show that we multiply by the respective stoichiometric coefficients now applying this we can use the same expression on the standard entropy change so applying this we get these from our data booklets or appendices this is going to be one one more of product multiplied by 9 .16 minus 2 multiplied by 3 3.

02:02 2.

02:03 So this gives us a standard enthalpy change of negative 57 .24 and this is in kilojoules.

02:11 Then we can do the same for the standard entropy change.

02:15 This is equal to 1 mole multiplied by the entropy change which is equal to 304 .4 minus 2 moles multiplied by 240 .1.

02:26 And this is going to be equal to negative 175 .8 and this is in joll's pair.

02:32 Now that we have our standard entropy change and our standard enthalpy change, we can then use this formula to determine the standard gives energy change, and we take the standard gives energy change and plug it in here to finally get our equilibrium constant...

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