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Multiple Choice
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
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.
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.
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: \( \frac{2.0 \text{ g}}{44.01 \text{ g/mol}} \).
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: \( -514.4 \text{ kJ} \times \frac{\text{moles of CO2}}{2} \).
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.