The reaction describing the formation of ozone from oxygen is shown below.
3 O2(g) <--> 2 O3(g)
Calculate Grxn at 288 K for this reaction in a flask where
[O2] = 3.419 x 10-2 M and
[O3] = 5.783 x 10-4 M.
Assume G° = 326 kJ.
Use molarity to construct the reaction quotient, and express your answer in kJ.
DG = DGo + RT*lnQ
Q = (O3)^2/(O2)^3
Use 8.314 for R
To calculate the standard Gibbs free energy change (ΔG°) for the reaction at 288 K, the equation we need to use is:
ΔG = ΔG° + RT ln(Q)
Where:
ΔG is the Gibbs free energy change at 288 K,
ΔG° is the standard Gibbs free energy change,
R is the gas constant (8.314 J/(mol·K) or 0.008314 kJ/(mol·K)),
T is the temperature in Kelvin, and
Q is the reaction quotient.
We are given the concentrations of O2 and O3, so we can calculate Q using the formula:
Q = ([O3]^2) / ([O2]^3)
Substituting the given concentrations:
Q = ((5.783 x 10^-4 M)^2) / ((3.419 x 10^-2 M)^3)
Performing the calculation:
Q = 1.327 x 10^-7 M^2 / (3.419 x 10^-2 M)^3
Now, we can substitute the known values into the equation for ΔG:
ΔG = 326 kJ + (0.008314 kJ/(mol·K) * 288 K) * ln(1.327 x 10^-7)
Calculating the natural logarithm:
ΔG = 326 kJ + 2.394 kJ * ln(1.327 x 10^-7)
Using a calculator to evaluate the natural logarithm and calculate ΔG:
ΔG ≈ 326 kJ + 2.394 kJ * (-16.317)
ΔG ≈ 326 kJ - 39.09 kJ
ΔG ≈ 286.91 kJ
Therefore, the Gibbs free energy change for the reaction at 288 K is approximately -286.91 kJ.