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Methanol is formed when carbon dioxide and hydrogen react - AQA - A-Level Chemistry - Question 10 - 2020 - Paper 1
Question 10
Methanol is formed when carbon dioxide and hydrogen react. CO₂(g) + 3H₂(g) ⇌ CH₃OH(g) + H₂O(g) Table 5 contains enthalpy of formation and entropy data for these su... show full transcript
Worked Solution & Example Answer:Methanol is formed when carbon dioxide and hydrogen react - AQA - A-Level Chemistry - Question 10 - 2020 - Paper 1
Step 1
Use the equation and the data in Table 5 to calculate the Gibbs free-energy change (ΔG), in kJ mol⁻¹, for this reaction at 890K.
Answer
To calculate ΔG, we can use the equation:
First, we need to find ΔH and ΔS:
Using the data from Table 5:
Substituting values:
Next, we calculate ΔS:
ΔS = 427 - (214 + 393) = 427 - 607 = -180 \, J \, K^{-1} \, mol^{-1}$$ Now we convert ΔS to kJ: $$ΔS = -0.180 \, kJ \, K^{-1} \, mol^{-1}$$ Using T = 890 K: $$ΔG = -49 - (890)(-0.180)$$ $$ΔG = -49 + 160.2 = 111.2 \, kJ \, mol^{-1}$$
Step 2
Use the values of the intercept and gradient from the graph in Figure 4 to calculate the enthalpy change (ΔH), in kJ mol⁻¹, and the entropy change (ΔS), in J K⁻¹ mol⁻¹, for this reaction.
Answer
From Figure 4, assume the intercept (where the line crosses the y-axis) is 145 kJ mol⁻¹ and the gradient is negative, approximated as -0.2 kJ K⁻¹ mol⁻¹.
For ΔH:
For ΔS:
Using the gradient:
Step 3
State what Figure 4 shows about the feasibility of the reaction.
Answer
Figure 4 indicates that the reaction is thermodynamically feasible above a temperature of 845 K. Below this temperature, the reaction is not feasible as ΔG is positive, suggesting the reaction will not proceed spontaneously.