Question

Calculate \(\Delta E\), and determine whether the process is endothermic or exothermic for the following cases: (a) A system absorbs \(105 \mathrm{~kJ}\) of heat from its surroundings while doing \(29 \mathrm{~kJ}\) of work on the surroundings; (b) \(q=1.50 \mathrm{~kJ}\) and \(w=-657 \mathrm{~J} ;\) (c) the system releases \(57.5 \mathrm{~kJ}\) of heat while doing \(22.5 \mathrm{~kJ}\) of work on the surroundings.

Short answer

(a) \(\Delta E = 134 \mathrm{~kJ}\) (endothermic); (b) \(\Delta E = 0.843 \mathrm{~kJ}\) (endothermic); (c) \(\Delta E = -35 \mathrm{~kJ}\) (exothermic)

Step-by-step solution

Identify the Given Values

For this case, q = +105 kJ (absorbed) and w = +29 kJ (work done on surroundings).

Calculate ΔE for Case (a)

Use the formula, ΔE = q + w: ΔE = (+105 kJ) + (+29 kJ) = 134 kJ

Determine if the Process is Endothermic or Exothermic

Since ΔE is positive, the process is endothermic. Case (b):

Identify the Given Values

For this case, q = +1.50 kJ (absorbed) and w = -657 J (work done by the system). Convert w to kJ: w = -657 J * (1 kJ / 1000 J) = -0.657 kJ

Calculate ΔE for Case (b)

Use the formula, ΔE = q + w: ΔE = (+1.50 kJ) + (-0.657 kJ) = 0.843 kJ

Determine if the Process is Endothermic or Exothermic

Since ΔE is positive, the process is endothermic. Case (c):

Identify the Given Values

For this case, q = -57.5 kJ (released) and w = +22.5 kJ (work done on surroundings).

Calculate ΔE for Case (c)

Use the formula, ΔE = q + w: ΔE = (-57.5 kJ) + (+22.5 kJ) = -35 kJ

Determine if the Process is Endothermic or Exothermic

Since ΔE is negative, the process is exothermic.