Calculate the Gibbs free energy change associated with the formation of 2.0 g of CO2 from the reaction: 2 CO(g) + O2(g) -> 2 CO2(g); given ΔG° = -514.4 kJ for the formation of 2 moles of CO2.

• A. -11.7 kJ
• B. -514.4 kJ
• C. -23.4 kJ
• D. -257.2 kJ

Answer: (A)

Verified step by step guidance

1. First, understand that the Gibbs free energy change (ΔG°) given is for the formation of 2 moles of CO2. We need to calculate the ΔG for the formation of 2.0 g of CO2.
2. Calculate the molar mass of CO2. The molar mass of carbon (C) is approximately 12.01 g/mol and that of oxygen (O) is approximately 16.00 g/mol. Therefore, the molar mass of CO2 is 12.01 + 2(16.00) = 44.01 g/mol.
3. Determine the number of moles of CO2 in 2.0 g. Use the formula: \( \text{moles of CO2} = \frac{\text{mass of CO2}}{\text{molar mass of CO2}} \). Substitute the values: \( \frac{2.0 \text{ g}}{44.01 \text{ g/mol}} \).
4. Calculate the Gibbs free energy change for the formation of the calculated moles of CO2. Use the proportion: \( \Delta G = \Delta G^\circ \times \frac{\text{moles of CO2}}{2 \text{ moles}} \). Substitute the values: \( -514.4 \text{ kJ} \times \frac{\text{moles of CO2}}{2} \).
5. Finally, solve the equation to find the Gibbs free energy change for the formation of 2.0 g of CO2. This will give you the desired ΔG value.