At a certain temperature, 514, Kp for the reaction,
Cl2(g) + Br2(g) <=> 2 BrCl(g), is 6.98 x 107.
Calculate the value of DGo in kJ for the reaction at 514 K.
To calculate the standard Gibbs free energy change (ΔG°) for a reaction at a given temperature, you can use the equation:
ΔG° = -RT ln(Kp)
where:
ΔG° is the standard Gibbs free energy change (in joules),
R is the gas constant (8.314 J/mol·K),
T is the temperature in Kelvin, and
Kp is the equilibrium constant.
In this case, you are given the equilibrium constant (Kp) and the temperature (514 K). To calculate ΔG°, follow these steps:
Step 1: Convert Kp to K
Since Kp is the equilibrium constant in terms of partial pressures, you need to convert it to K, which represents the equilibrium constant in terms of concentrations. To do this conversion, you need to know the molar concentrations of the reactants and products.
Step 2: Writing the balanced equation
The balanced equation for the reaction is given as follows:
Cl2(g) + Br2(g) <=> 2 BrCl(g)
Step 3: Calculating K
Kp is related to K by the equation:
Kp = K (RT)^Δn
where Δn is the difference in stoichiometric coefficients between the products and reactants. In this case, Δn = 2 - (1+1) = 0.
Therefore, K = Kp / (RT)^Δn
= 6.98 x 10^7 / (8.314 J/mol·K * 514 K)^0
= 3.9771 x 10^4
Step 4: Calculating ΔG°
Now that we have K, we can calculate ΔG° using the equation:
ΔG° = -RT ln(K)
= -(8.314 J/mol·K * 514 K) * ln(3.9771 x 10^4)
= -10756.492 J
Finally, to convert this value to kilojoules (kJ), divide by 1000:
ΔG° = -10.756 kJ
Therefore, the value of ΔG° for the reaction at 514 K is -10.756 kJ.