Problem 26 - Chemistry: The Central Science

Question

For the following processes, calculate the change in internal energy of the system and determine whether the process is endothermic or exothermic: (a) A balloon is heated by adding 850 J of heat. It expands, doing $382 \mathrm{~J}\( of work on the atmosphere. (b) A \)50-g$ sample of water is cooled from \(30^{\circ} \mathrm{C}\) to \(15^{\circ} \mathrm{C}\), thereby losing approximately \(3140 \mathrm{~J}\) of heat. (c) A chemical reaction releases \(6.47 \mathrm{~kJ}\) of heat and does no work on the surroundings.

Step-by-Step Solution

Answer

(a) The change in internal energy is \(∆U = 468 \mathrm{~J}\), and the process is endothermic. (b) The change in internal energy is \(∆U = -3140 \mathrm{~J}\), and the process is exothermic. (c) The change in internal energy is \(∆U = -6470 \mathrm{~J}\), and the process is exothermic.

Step 1: (a) Calculate the change in internal energy

: Given that 850 J of heat is added to the balloon (Q = 850 J) and the balloon expands, doing 382 J of work (W = 382 J). We can now find the change in internal energy using the previously discussed equation: ∆U = Q - W ∆U = 850 J - 382 J ∆U = 468 J Since Q > 0, the process is endothermic.

Step 2: (b) Calculate the change in internal energy of cooling water

: In this case, the 50-g sample of water loses 3140 J of heat (Q = -3140 J). There is no work done, so W = 0. We can find the change in internal energy using the same equation: ∆U = Q - W ∆U = -3140 J - 0 ∆U = -3140 J Since Q < 0, the process is exothermic.

Step 3: (c) Calculate the change in internal energy of the chemical reaction

: For this problem, the chemical reaction releases 6.47 kJ of heat (Q = -6470 J, we use negatives since it's released). Since there is no work done on the surroundings (W = 0), we can find the change in internal energy using the same equation: ∆U = Q - W ∆U = -6470 J - 0 ∆U = -6470 J As Q < 0, the process is exothermic.