a. Calculate the delta H, delta G, and equilibrium constant for the reaction of methane with Cl2 to give CH3Cl and HCl. Use the following information for your calculations:
Bond Dissociation Energies:
CH3-H (104.8kcal/mol), Cl-Cl(59.0 kcal/mol), CH3-Cl(85.0 kcal/mol), and H-Cl (103.2 kcal/mol).
Thermodynamic data:
DeltaSrxn= + 0.29 x 10^.3 kcal/mol K, T=0 degrees celcius, and R= 1.987 cal/mol
Find delta H? kcal/mol
find delta G? kcal/mol
and find what K=
To calculate the delta H (change in enthalpy), delta G (change in Gibbs free energy), and equilibrium constant (K) for the reaction, we will use the following equations:
delta H = ∑(Bonds Broken) - ∑(Bonds Formed)
delta G = delta H - T * delta S
K = e^(-delta G / (R * T))
First, let's calculate delta H.
The reaction can be represented as follows:
CH4 + Cl2 → CH3Cl + HCl
Bond dissociation energy represents the energy required to break 1 mole of a specific bond in a gaseous molecule.
According to the information provided, the bonds broken are:
1 mol of CH4-H (104.8 kcal/mol)
1 mol of Cl-Cl (59.0 kcal/mol)
The bonds formed are:
1 mol of CH3-Cl (85.0 kcal/mol)
1 mol of H-Cl (103.2 kcal/mol)
delta H = (1 * (CH3-H) + 1 * (Cl-Cl)) - (1 * (CH3-Cl) + 1 * (H-Cl))
Substituting the given bond dissociation energy values:
delta H = (1 * 104.8) + (1 * 59.0) - (1 * 85.0 + 1 * 103.2)
delta H = 163.8 - 188.2
delta H = -24.4 kcal/mol
Therefore, delta H = -24.4 kcal/mol.
Next, let's calculate delta G.
delta G = delta H - T * delta S
Given:
delta S = 0.29 x 10^3 kcal/mol K (convert to kcal/mol K by multiplying by 1000)
T = 0°C = 273.15 K
R = 1.987 cal/mol
delta G = -24.4 - (0.29 x 10^3) * 273.15 / (1000 * 1.987)
Calculating the value:
delta G = -24.4 - 79.35345 / 1.987
delta G = -24.4 - 39.97
delta G = -64.37 kcal/mol
Therefore, delta G = -64.37 kcal/mol.
Finally, let's calculate K.
K = e^(-delta G / (R * T))
Substituting the values:
K = e^(-(-64.37) / (1.987 * 273.15))
Calculating the value:
K = e^(64.37 / (1.987 * 273.15))
K = e^(0.11532)
Therefore, K ≈ 1.1229.
In summary:
delta H ≈ -24.4 kcal/mol
delta G ≈ -64.37 kcal/mol
K ≈ 1.1229