Nitrosyl chloride (NOCl) decomposes at high temperature. The equation is
2 NOCl (g) -> 2 NO (g) + Cl2 (g) at 227C
Using delta H = 81.2 kJ and delta S = 128 J/K, calculate the value of the equilibrium constant for this reaction.
a 1.60 X 10-2
b. 2.1 X 10-7
c. 62.8
d. 4.9 X 106
e. 3,20 X 109
help no idea?
To calculate the equilibrium constant (K) for the given reaction, we can use the formula:
ΔG° = -RT ln(K)
where ΔG° is the standard Gibbs free energy change, R is the gas constant (8.314 J/(mol·K)), T is the temperature in Kelvin, and ln is the natural logarithm.
Firstly, we need to convert the given temperature from Celsius to Kelvin:
227 °C + 273.15 = 500.15 K
Next, we need to calculate the ΔG° using the formula:
ΔG° = ΔH° - TΔS°
Given:
ΔH° = 81.2 kJ/mol
ΔS° = 128 J/(mol·K)
T = 500.15 K
Converting the units:
ΔH° = 81.2 kJ/mol × 1000 J/1 kJ = 81,200 J/mol
Now, substitute the values into the equation:
ΔG° = (81,200 J/mol) - (500.15 K)(128 J/(mol·K))
ΔG° = 81,200 J/mol - 64,012 J/mol
ΔG° = 17,188 J/mol
Now, we can substitute ΔG° into the equation for K:
ΔG° = -RT ln(K)
17,188 J/mol = -(8.314 J/(mol·K))(500.15 K) ln(K)
Simplifying the equation:
ln(K) = -(17,188 J)/(8.314 J/mol·K)(500.15 K)
ln(K) = -4.121
Now, we can solve for K by taking the natural exponent (e) of both sides:
K = e^(-4.121)
K ≈ 0.0160
The value of the equilibrium constant (K) for this reaction is approximately 0.0160 or 1.60 × 10^-2. Therefore, the correct answer is option a) 1.60 × 10^-2.
To calculate the equilibrium constant (K) for the given reaction, we can use the equation:
ΔG = ΔH - TΔS
where ΔG is the change in Gibbs free energy, ΔH is the change in enthalpy, ΔS is the change in entropy, and T is the temperature in Kelvin.
At equilibrium, ΔG = 0. Therefore, we can rewrite the equation as:
0 = ΔH - TΔS
Solving for TΔS, we get:
TΔS = ΔH
Now let's plug in the given values:
ΔH = 81.2 kJ = 81,200 J (convert kJ to J)
ΔS = 128 J/K
T = 227°C = 500 K (convert °C to K)
TΔS = 81,200 J
Now let's calculate the equilibrium constant (K) using the formula:
K = e^(-ΔG/RT), where R is the gas constant (8.314 J/mol·K)
K = e^(-ΔH/RT) * e^(ΔS/R)
K = e^(-81,200 J/(8.314 J/mol·K * 500 K)) * e^(128 J/K / (8.314 J/mol·K))
K ≈ e^(-163.80) * e^(15.40)
K ≈ 1.87 × 10^-71
So, the value of the equilibrium constant for this reaction is approximately 1.87 × 10^-71.
None of the given options match this value exactly.