Consider the reaction
2 SO2 + O2 in equilibrium with 2 SO3 .
At 25°C Ho = -197.78 kJ and So = -187.95 J/K. Using this information, calculate the equilibrium constant for the reaction at 50°C. (R = 8.314 J/K)
Enter your answer using TWO significant figures.
To calculate the equilibrium constant (K) at a different temperature, we can use the Van't Hoff equation:
ln(K2/K1) = ΔH°/R * (1/T1 - 1/T2)
Where:
K1 = equilibrium constant at temperature T1
K2 = equilibrium constant at temperature T2
ΔH° = standard enthalpy change of the reaction
R = gas constant (8.314 J/K)
T1 = initial temperature
T2 = final temperature
First, let's plug in the given values:
ΔH° = -197.78 kJ = -197780 J (we convert kJ to J)
T1 = 25°C = 25 + 273 = 298 K (we convert °C to K)
T2 = 50°C = 50 + 273 = 323 K (we convert °C to K)
Now, we can calculate the equilibrium constant at the final temperature using the Van't Hoff equation:
ln(K2/K1) = ΔH°/R * (1/T1 - 1/T2)
ln(K2/1) = ΔH°/R * (1/T1 - 1/T2)
ln(K2) = ΔH°/R * (1/T1 - 1/T2)
K2 = e^(ΔH°/R * (1/T1 - 1/T2))
K2 = e^((-197780 J)/(8.314 J/K) * (1/298 K - 1/323 K))
Now, let's calculate K2 using the above formula:
K2 = e^(-7689.63)
K2 ≈ 1.13
Therefore, the equilibrium constant for the reaction at 50°C is approximately 1.13.