Determine Δ_fG° at 298 K for SnO using the data below. Sn(s) + SnO₂(s) → 2SnO(s)
Given: Δ_rG° = 12.0 kJ/mol-rxn at 298K.
Substance
Δ_fG°(kJ/mol) at 298 K
SnO(s)
?
SnO₂(s)
-515.8

Question

Quizplus · Accepted Answer

We can use the relationship ΔS1U1B1fS1U1B0G° = ΣnΔS1U1B1fS1U1B0G°(products) - ΣmΔS1U1B1fS1U1B0G°(reactants), where n and m are the coefficients from the balanced chemical equation.

For the given reaction, the only product is SnO and its standard state is solid. Therefore, ΔS1U1B1fS1U1B0G°(SnO) = 0.

The reactants are Sn(s) and SnOS1U1B12S1U1B0(s), and their standard state enthalpies of formation are 0 and -515.8 kJ/mol, respectively.

Thus, ΔS1U1B1fS1U1B0G° = (2)(0 kJ/mol) - (1)(-515.8 kJ/mol) = 515.8 kJ/mol.

However, we are asked for ΔS1U1B1fS1U1B0G° at 298 K, not 0 K. We can use the relationship ΔS1U1B1rxnS1U1B0H° = ΔS1U1B1rxnS1U1B0H°(298) - ΣnCp,mΔT, where Cp,m is the molar heat capacity at constant pressure and ΔT is the change in temperature from 0 K to 298 K.

Assuming that the molar heat capacities are constant over the temperature range, we can estimate ΔS1U1B1rxnS1U1B0H°(298) as follows:

ΔS1U1B1rxnS1U1B0H°(298) ≈ ΔH1U1B1rxnS1U1B0H°(298) - TΔS1U1B1rxnS1U1B0G°(298)
≈ (12.0 kJ/mol) - (298 K)(515.8 J/mol-K)(1 kJ/1000 J)
≈ -251.9 kJ/mol

Therefore, the answer is A, -251.9 kJ/mol.

Determine ΔfG° at 298 K for SnO Using the Data

Determine Δ_fG° at 298 K for SnO Using the Data