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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 the Gibbs free-energy change (ΔG) for the reaction, we use the formula:
Where:
From the data in Table 5:
- For products (CH₃OH and H₂O):
- ΔH(CH₃OH) = -201 kJ/mol
- ΔH(H₂O) = -242 kJ/mol
Total ΔH for products = -201 + (-242) = -443 kJ/mol
- For reactants (CO₂ and H₂):
- ΔH(CO₂) = -394 kJ/mol
- ΔH(H₂) = 0 kJ/mol
Total ΔH for reactants = -394 + 0 = -394 kJ/mol
Now substituting into the ΔH equation:
Next, we calculate the ΔS. The entropy change for the reaction can be calculated as:
From Table 5:
- S(CH₃OH) = 238 J/K·mol
- S(H₂O) = 189 J/K·mol
- S(CO₂) = 214 J/K·mol
- S(H₂) = 131 J/K·mol
Total S for products = 238 + 189 = 427 J/K·mol Total S for reactants = 214 + 131 = 345 J/K·mol
Now substituting into the ΔS equation:
Finally, substituting ΔH and ΔS into the Gibbs equation:
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 the graph in Figure 4,
- The intercept on the ΔG axis (where T = 0) is approximately 145 kJ/mol.
- The gradient of the line (ΔG vs Temperature) is approximately -0.167 kJ/mol/K.
-
Enthalpy change (ΔH):
-
The entropy change (ΔS) can be calculated using the gradient:
Step 3
State what Figure 4 shows about the feasibility of the reaction.
Answer
Figure 4 indicates that the Gibbs free-energy change (ΔG) is negative at temperatures above approximately 845 K, suggesting that the reaction is thermodynamically feasible at these temperatures.
Conversely, at temperatures below 845 K, the reaction becomes non-feasible, indicating that it does not proceed spontaneously.