N2 + 3H2 --> 2NH3

At 25°C (delta)Ho = -92.22 kJ and (delta)So = -198.53 J/K. Using this information, calculate the equilibrium constant for the reaction at 2.43x10^2°C. (R = 8.314 J/K)

Apparently the way I'm doing it is wrong:

I divide 198.53 by 1000 then multiply by 298 to get delta(S). Then I subtract this from delta(H) to get delta(G). Then I multiply 516 with .008314... I take this answer and divide delta(G) by it, then multiply by -1. I take this to the e power... Then I use the equation Kc = (RT)^-n * Kp to get the equilibrium constant. However my answer is still wrong.

or mike or whomever,

Two points:
1. How do you know to calculate Kc instead of Kp? The problem doesn't specify which. Since this is a gaseous reaction, Kp may be what they are looking for.

2. Have you tried the van't Hoff equation. You have delta H and one T so the van't Hoff equation can be used to calculate K at any other T.

To calculate the equilibrium constant for the given reaction at a temperature of 2.43x10^2°C, we need to use the thermodynamic data provided and apply the correct formula. Let's break down the steps:

Step 1: Convert the temperature to Kelvin
To convert the temperature from °C to Kelvin, add 273.15. In this case, 2.43x10^2°C is equal to 2.43x10^2 + 273.15 = 545.15 K.

Step 2: Calculate ΔG (change in Gibbs free energy)
ΔG = ΔH - TΔS, where ΔH is the change in enthalpy, and ΔS is the change in entropy.

Given:
ΔH = -92.22 kJ (convert to J: -92.22 kJ * 1000 J/kJ = -92,220 J)
ΔS = -198.53 J/K

ΔG = -92,220 J - (545.15 K * (-198.53 J/K))
ΔG = -92,220 J + 108,251.6995 J
ΔG ≈ 16,031 J (approximately)

Step 3: Calculate the equilibrium constant (Kc)
Use the equation: ΔG = -RT * ln(Kc), where R is the gas constant (8.314 J/K).

R = 8.314 J/K
T = 545.15 K
ΔG = 16,031 J

16,031 J = -8.314 J/K * 545.15 K * ln(Kc)
ln(Kc) = 16,031 J / (-8.314 J/K * 545.15 K)
ln(Kc) ≈ -0.0366

Taking the exponent (e) of both sides:
Kc ≈ e^-0.0366

Using a calculator or software, calculate e^-0.0366:
Kc ≈ 0.9646

Therefore, the equilibrium constant (Kc) for the given reaction at a temperature of 2.43x10^2°C is approximately 0.9646.

To calculate the equilibrium constant (Kc) for the given reaction at 2.43x10^2°C, you need to follow these steps:

Step 1: Convert the temperature to Kelvin
2.43x10^2°C = 2.43x10^2 + 273.15 = 473.15 K

Step 2: Calculate ΔG (change in Gibbs free energy)
ΔG = ΔH - TΔS

Remember that ΔH = -92.22 kJ and ΔS = -198.53 J/K. So, we need to convert ΔH to J and ΔS to kJ.

ΔH = -92.22 kJ × 1000 J/kJ = -92,220 J
ΔS = -198.53 J/K ÷ 1000 kJ/J = -0.19853 kJ/K

ΔG = -92,220 J - 473.15 K × (-0.19853 kJ/K)
= -92,220 J + 93.89 kJ
= -92,220 J + 93,890 J
= 1,670 J

Step 3: Calculate Kp (equilibrium constant in terms of partial pressures)
Kp = e^(-ΔG / (RT))

Remember that R = 8.314 J/K and T = 473.15 K.

Kp = e^(1,670 J / (8.314 J/K × 473.15 K))
= e^(1,670 / (8.314 × 473.15))
= e^(1,670 / 3917.866)
≈ e^0.426244

Step 4: Calculate Kc (equilibrium constant in terms of concentrations)
Kc = Kp × ((RT)^-Δn)

Δn is the change in the number of moles of gas, which is given by the stoichiometry of the balanced equation. In this case, Δn = (2 - (1 + 3)) = -2.

Kc = Kp × ((RT)^2)
= e^0.426244 × ((8.314 J/K × 473.15 K)^-2)

Now you can calculate the value of Kc using the given values.

Please note that in this step, you need to accurately calculate the exponential part to get the correct result.