Calculating Entropy for Ideal Gas Reaction

[Denver Dang]

Homework Statement

Hi...

I have a problem I'm a bit stuck with.

It says

For the ideal gas reaction:

$$2\mathrm{A}\left( g \right)+\mathrm{B}\left( g \right)\leftrightarrow 4\mathrm{C}\left( g \right)$$

one has measured the temperature dependence of the equilibrium constant to be:

$$K(T) = 10 +aT$$
where $a=1.00\cdot {{10}^{-3}}{{\mathrm{K}}^{-1}}$ in the interval 280 K < T < 310 K.

Besides that I know the Helmholtz Free Energy, ${{\Delta }_{r}}\mathrm{A}{}^\circ$.

Now, calculate the entropy ${{\Delta }_{r}}\mathrm{S}$ for the reaktion at T = 298 K and P = 1.00*10^-3 bar.

Homework Equations

Not quite sure.

The Attempt at a Solution

I'm pretty stuck. I've tried with combining the relations between Helmholtz Free Energy, Gibbs Energy, Enthalpy to see if I could come up with anything. But nothing gave the right answer, which is supposed to be 77.1 J/(K*mol).

So maybe one of you out there could point me in the right direction ?


Regards

 

[nate808]

I would start by looking at the given information and equations to see if there are any relationships that can be used to solve the problem. The first thing that stands out to me is the temperature dependence of the equilibrium constant, K(T). This equation tells us that as the temperature increases, the equilibrium constant also increases.

Next, I would look at the equation for calculating the entropy, {{\Delta }_{r}}\mathrm{S}. This equation involves the equilibrium constant, temperature, and pressure. Since we are given the temperature and pressure, we just need to find the equilibrium constant for T = 298 K and P = 1.00*10-3 bar.

To find the equilibrium constant, we can use the given information and equations. We know that at T = 298 K, a = 1.00*10^-3 K^-1, so we can substitute this value into the equation for K(T) to get K(298) = 10 + (1.00*10^-3 * 298) = 10.298.

Now, we have all the information we need to calculate {{\Delta }_{r}}\mathrm{S}. We can plug in the values for K, T, and P into the equation and solve for {{\Delta }_{r}}\mathrm{S}. It should come out to be 77.1 J/(K*mol), which is the expected answer.

In summary, the key steps to solving this problem are to identify the given information and equations, use the temperature dependence of the equilibrium constant to find the equilibrium constant at T = 298 K, and then plug in all the values into the equation for {{\Delta }_{r}}\mathrm{S}.