Step 1: Understand the given information : In the bomb calorimeter: 𝑞 = − 13.1 kJ q = − 13.1 kJ (negative because heat is released). In the coffee-cup calorimeter: 𝑞 = 11.0 kJ q = 11.0 kJ (positive because heat is absorbed). Both measurements are for the same reaction with the same amount of reactant. Understand the difference between bomb calorimeter and coffee-cup calorimeter : Bomb calorimeter measures the change in internal energy ( Δ 𝑈 Δ U ). Coffee-cup calorimeter measures the change in enthalpy ( Δ 𝐻 Δ H ). Relate internal energy change ( Δ 𝑈 Δ U ) and enthalpy change ( Δ 𝐻 Δ H ) : For a reaction at constant pressure ( 𝑃 P ), the relationship between Δ 𝑈 Δ U and Δ 𝐻 Δ H is: Δ 𝐻 = Δ 𝑈 + 𝑃 Δ 𝑉 Δ H = Δ U + P Δ V . In the bomb calorimeter, Δ 𝑉 Δ V (change in volume) is essentially zero because the reaction takes place under constant volume conditions. So, Δ 𝐻 ≈ Δ 𝑈 Δ H ≈ Δ U . Determine which value corresponds to the bomb calorimeter : Since Δ 𝐻 Δ H in the coffee-cup calorimeter will be slightly larger than Δ 𝑈 Δ U in the bomb calorimeter due to the positive Δ 𝑉 Δ V , the value obtained in the bomb calorimeter would be the one with the smaller magnitude. Compare the magnitudes of 𝑞 q values : ∣ 𝑞 bomb ∣ = ∣ − 13.1 kJ ∣ = 13.1 kJ ∣ q bomb ∣ = ∣ − 13.1 kJ ∣ = 13.1 kJ ∣ 𝑞 coffee-cup ∣ = ∣ 11.0 kJ ∣ = 11.0 kJ ∣ q coffee-cup ∣ = ∣11.0 kJ ∣ = 11.0 kJ Conclusion : The smaller magnitude value, 13.1 kJ 13.1 kJ , corresponds to the bomb calorimeter. Explanation: So, the value obtained in the bomb calorimeter is − 13.1 kJ − 13.1 kJ . Step 2: We have two measurements: 𝑞 = − 13.1 kJ q = − 13.1 kJ 𝑞 = 11.0 kJ q = 11.0 kJ Given that the same reaction is conducted in both the bomb calorimeter and the coffee-cup calorimeter, we can infer the following: In the bomb calorimeter, the measured heat ( 𝑞 q ) corresponds to the internal energy change ( Δ 𝑈 Δ U ) of the reaction. In the coffee-cup calorimeter, the measured heat ( 𝑞 q ) corresponds to the enthalpy change ( Δ 𝐻 Δ H ) of the reaction. The negative sign in 𝑞 = − 13.1 kJ q = − 13.1 kJ indicates that heat is being released by the reaction. This suggests that − 13.1 kJ − 13.1 kJ is the internal energy change ( Δ 𝑈 Δ U ) of the reaction, which would be measured in the bomb calorimeter. Explanation: Therefore, the value − 13.1 kJ − 13.1 kJ was obtained in the bomb calorimeter, not the coffee-cup calorimeter. Final Answer: Which value was obtained in the bomb calorimeter? Given that the same reaction is conducted in both the bomb calorimeter and the coffee-cup calorimeter, and knowing that the reaction releases energy, the value obtained in the bomb calorimeter would be the one with the negative sign. So, the value obtained in the bomb calorimeter is 𝑞 = − 13.1 kJ q = − 13.1 kJ .

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