Consider the reaction
2 SO2(g) + O2(g) in equilibrium with 2 SO3(g) .
At 25°C delta H° = -197.78 kJ and delta S° = -187.95 J/K. Using this information, calculate the equilibrium constant for the reaction at -32°C. (R = 8.314 J/K)
Enter your answer using TWO significant figures. You may use scientific notation with an "e" if necessary (e.g. 1.2e34).
dG = dH - TdS
Then dG = -RTlnK
Calculate K
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To calculate the equilibrium constant for the reaction at -32°C, we can use the equation:
ln(K2/K1) = (ΔH°/R) * [(1/T1) - (1/T2)]
Where:
- ln represents the natural logarithm
- K2/K1 is the ratio of the equilibrium constants at two different temperatures
- ΔH° is the standard enthalpy change for the reaction
- R is the ideal gas constant (8.314 J/K)
- T1 and T2 are the initial and final temperatures in Kelvin, respectively.
Let's calculate the equilibrium constant at -32°C (-305.15 K).
First, we need to find the ratio of equilibrium constants (K2/K1):
ln(K2/K1) = (ΔH°/R) * [(1/T1) - (1/T2)]
ln(K2/K1) = (-197.78 kJ / -305.15 K) * [(1 / 298.15 K) - (1 / -305.15 K)]
Now we can calculate the value inside the parentheses:
(1 / 298.15 K) - (1 / -305.15 K) = 0.00334
Substituting this value back into the equation:
ln(K2/K1) = (-197.78 kJ / -305.15 K) * 0.00334
ln(K2/K1) = 0.002162
Now we can find the ratio of equilibrium constants (K2/K1):
K2/K1 = e^(ln(K2/K1))
K2/K1 = e^(0.002162)
Finally, we can find the equilibrium constant K2:
K2 = K1 * (K2/K1)
K2 = K1 * e^(0.002162)
Since the value of K1 is not provided, we cannot calculate the exact value of K2. However, we can provide the equation to calculate it once you have the value of K1.