Estimate the value of the equilibrium constant at 655 K for each reaction in Problem 74. (ΔHf^∘

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

Key Concepts

Temperature Dependence of Equilibrium Constants

The equilibrium constant is temperature-dependent, and this relationship is quantitatively described by the van’t Hoff equation. This equation relates the change in the equilibrium constant with temperature to the reaction enthalpy, allowing for estimation of equilibrium constants at temperatures other than the standard state.

Van’t Hoff Equation

The van’t Hoff equation is a mathematical formula that connects the temperature dependence of the equilibrium constant to the enthalpy change of the reaction. By plotting the natural logarithm of the equilibrium constant against the inverse of the temperature, one can determine the reaction enthalpy and predict how the equilibrium will shift with changes in temperature.

Equilibrium Constant

The equilibrium constant is a dimensionless value that expresses the ratio of the concentrations or partial pressures of products to reactants at equilibrium. It provides vital insight into the position of equilibrium and the extent of a reaction under defined conditions, enabling predictions about the behavior of a chemical system as the reaction proceeds to equilibrium.

Standard Enthalpy of Formation

The standard enthalpy of formation refers to the heat change that occurs when one mole of a compound is formed from its constituent elements in their standard states. This thermodynamic quantity is essential for calculating reaction enthalpies and subsequently helps in understanding and predicting the energy changes associated with chemical reactions.

Transcript

00:01 All right, so for this one, we're trying to find the equilibrium constant k for at 655 kelvin for some reactions that we looked at earlier in problem 74.

00:17 And so we'll start with the first reaction, which is 2n02 going to n204.

00:34 And so the first thing i would do is think back to how do we calculate.

00:42 The equilibrium constant k.

00:44 And so you look at this formula, delta g equals delta g not plus r t ln of k.

01:00 And so we can calculate delta g not and we can also estimate delta g if we know delta h not and delta s not and r is a constant and then t is 655.

01:12 So from there, once we find delta g not and delta g we can get what k is by solving the algebra.

01:18 And so that's what we'll do.

01:20 So to find delta g not, you do delta g of formation of the products minus delta g of formation of the reactants, accounting for the molar ratios.

01:32 So you can find these values in your textbook.

01:35 I'm just going to write them down 99 .8 minus 2 times 51 .3.

01:46 And that equals minus 2 .8 kilojoules.

01:49 So let's find delta h not using the same process of 9 .16 minus 2 times 33 .2 equals minus 57 .24 kilojoules.

02:16 And we'll do delta s up here real quick.

02:19 Delta s not equals 304 .4 .4 minus two times.

02:30 240 .1 and that comes out to be if you convert to kilojoules it's minus 0 .1758 kilojoules per kelvin of values so we can plug in and find out estimate what delta g is so delta g is approximately delta h0 minus 655 which is a temperature times delta s not and so if you plug those values in you'll get approximately 57 .9 and so from here we can solve the equation to find the equilibrium constant k so 57 .9 and that's in kilojoules equals minus 2 .8 plus the constant which in kilojoules is 0 .008 314 kilogels per mole kelvin times 655 times the natural log of k.

04:10 And so we can just solve for this and so we end up getting 60 .7 equals 5 .45 natural log of k.

04:25 If you raise both powers to e, k equals 6171 .2...

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