Question

Determine ∆g° for a reaction when ∆g = -138.2 kj/mol and q = 0.043 at 298 k. (r = 8.314 j/mol ･ k)

Answer 1

To determine ΔG° for a reaction, we can use the equation: ΔG° = ΔH° - TΔS°. Given ΔG = -138.2 kJ/mol, q = 0.043 at 298 K, and r = 8.314 J/mol·K, we can substitute the values into the equation and solve for ΔG° as follows: ΔG° = -138.2 kJ/mol - (298 K)(-8.314 J/mol·K)(ln(0.043)) = -138.2 kJ/mol + 67.47 kJ/mol = -70.73 kJ/mol

Step-by-step explanation:

To determine ΔG° for a reaction, we can use the equation: ΔG° = ΔH° - TΔS°. Given ΔG = -138.2 kJ/mol, q = 0.043 at 298 K, and r = 8.314 J/mol·K, we can substitute the values into the equation and solve for ΔG° as follows:

ΔG° = -138.2 kJ/mol - (298 K)(-8.314 J/mol·K)(ln(0.043)) = -138.2 kJ/mol + 67.47 kJ/mol = -70.73 kJ/mol

Answer 2

To determine ΔG°, the Gibbs free energy equation is used: ΔG = ΔG° + RTlnQ. Substituting the given values and performing calculations give ΔG° as approximately -138.09 kJ/mol.

Step-by-step explanation:

To determine the standard free energy change (ΔG°) for the reaction when ΔG is -138.2 kJ/mol and Q (reaction quotient) is 0.043 at 298 K, we can use the following relationship derived from the Gibbs free energy equation:

ΔG = ΔG° + RTlnQ

Rearranging the formula to solve for ΔG°, we get:

ΔG° = ΔG - RTlnQ

Substitute the given values into the equation:

• ΔG = -138.2 kJ/mol
• R = 8.314 J/mol·K (Note: 1 J = 0.001 kJ)
• T = 298 K
• Q = 0.043

ΔG° = (-138.2 kJ/mol) - (8.314 J/mol·K) × 298 K × ln(0.043) × (1 kJ/1000 J)

First converting R to kJ by multiplying by 0.001:

R = 8.314 J/mol·K × 0.001 kJ/J = 0.008314 kJ/mol·K

Now calculate the term RTlnQ:

RTlnQ = 0.008314 kJ/mol·K × 298 K × ln(0.043) = -0.111 kJ/mol (approximately)

Then we substitute and find ΔG°:

ΔG° = -138.2 kJ/mol - (-0.111 kJ/mol) = -138.09 kJ/mol (approximately)

The standard free energy change for the reaction is approximately -138.09 kJ/mol.