Question

Consider the reaction at 298 K:

2 H₂S(g) + SO₂(g) → 3 S(s) + 2 H₂O(g). Calculate ΔGrxn under these conditions:
P∨H₂S = 2.00 atm; P∨SO₂ = 1.50 atm; P∨H₂O = 0.0100 atm. Is the reaction more or less spontaneous under these conditions compared to the standard conditions?
a) More spontaneous
b) Less spontaneous
c) Equally spontaneous
d) Cannot be determined

Answer 1

To calculate the actual Gibbs free energy change for non-standard conditions, use the reaction quotient and the standard Gibbs free energy change formula, incorporating the given partial pressures. The sign of the actual Gibbs free energy change will indicate if the reaction is spontaneous. Without the value of ΔG°, the comparison to standard conditions cannot be made.

Step-by-step explanation:

The standard Gibbs free energy change (ΔG°) of a reaction can be calculated using the standard enthalpy (ΔH°) and standard entropy (ΔS°) changes of the reaction at a given temperature (T) using the formula:

ΔG° = ΔH° - T·ΔS°

However, to calculate the actual Gibbs free energy change (ΔGrxn) for non-standard conditions, we must use the reaction quotient (Q) as follows:

ΔGrxn = ΔG° + RT ln(Q)

where R is the gas constant (8.314 J/mol·K) and Q is the reaction quotient, calculated from the partial pressures of the gases involved.

Reaction quotient (Q): Q = (PˈH₂O)^2 / (PˈH₂S)^2·(PˈSO₂)

Substituting the given pressures:

Q = (0.0100 atm)^2 / (2.00 atm)^2·(1.50 atm) = 1.67×10⁻₆

Since ΔG° is not given for the reaction, we assume it is known or has been previously calculated at the standard conditions.

We then substitute the values into the ΔGrxn equation and calculate. If ΔGrxn is negative, the reaction is spontaneous under the given conditions. If it is positive, the reaction is nonspontaneous. The reaction is more spontaneous under the current conditions if ΔGrxn here is more negative than ΔG°, or less spontaneous if it is less negative or positive. Without the value of ΔG°, we cannot determine whether the reaction is more or less spontaneous compared to standard conditions.

Answer 2

To calculate ΔGrxn under given conditions, use the equation ΔGrxn = ΔGrxn° + RTln(Q), where Q is the reaction quotient calculated from partial pressures. If ΔGrxn is negative, the reaction is more spontaneous under the given conditions.

Step-by-step explanation:

To calculate ΔGrxn under the given conditions, we can use the equation: ΔGrxn = ΔGrxn° + RTln(Q). ΔGrxn° represents the standard free energy change, R is the gas constant (8.314 J/mol·K), T is the temperature in Kelvin (298 K), and Q is the reaction quotient. The reaction quotient can be calculated using the given partial pressures: Q = (PH₂S)^2 * (PSO₂) / (PH₂O)^2.

Once we have Q, we can substitute the values into the equation and solve for ΔGrxn. If ΔGrxn is negative, the reaction is more spontaneous under the given conditions compared to standard conditions. If ΔGrxn is positive, the reaction is less spontaneous.