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Chapter 5: Problem 34

(a) Under what condition will the enthalpy change of a process equal the amount of heat transferred into or out of the system? (b) During a constant- pressure process, the system releases heat to the surroundings. Does the enthalpy of the system increase or decrease during the process? (c) In a constant-pressure process, \(\Delta H=0 .\) What can you conclude about \(\Delta E, q,\) and \(w ?\)

Short Answer

Expert verified
(a) The enthalpy change, \(\Delta H\), equals the amount of heat transferred, \(q\), at constant pressure (\(\Delta H = q_P\)). (b) In a constant-pressure process with heat release, the enthalpy decreases, as both \(q\) and \(\Delta H\) are negative. (c) When \(\Delta H = 0\) in a constant-pressure process, the heat exchanged (\(q\)) is equal to the difference between the work done by the gas on its surroundings (\(w\)) and the pressure-volume work done (\(P\Delta V\)).

Step by step solution

01

(a) Condition when enthalpy change equals heat transferred

The enthalpy change of a process, \(\Delta H\), is equal to the amount of heat transferred into or out of the system (\(q\)), under the condition of constant pressure. Mathematically, this can be written as: \[ \Delta H = q_P, \] where \(q_P\) is the heat transferred at constant pressure.
02

(b) Enthalpy change during a constant-pressure process with heat release

During a constant-pressure process, the system releases heat to the surroundings. This means that the heat transfer is negative (\(q < 0\)). According to the equation stated earlier, \(\Delta H = q_P\), the enthalpy change will also be negative (\((ΔH < 0)\)) during the process. Therefore, the enthalpy of the system decreases during the process.
03

(c) Analysing the relationship between \(\Delta H\), \(\Delta E\), \(q\), and \(w\) when \(\Delta H=0\)

In a constant-pressure process, the enthalpy change is related to the internal energy change, heat, and work as follows: \[ \Delta H = \Delta E + P\Delta V, \] where \(\Delta E\) is the change in internal energy, \(P\) is the constant pressure, and \(\Delta V\) is the change in volume. When \(\Delta H = 0\), the equation becomes: \[ 0 = \Delta E + P\Delta V. \] Considering the first law of thermodynamics, which relates internal energy change, heat, and work, we have: \[ \Delta E = q - w, \] where \(w\) is the work done by the gas on its surroundings. By substituting this expression for \(\Delta E\) into the equation for constant pressure, we obtain: \[ 0 = (q - w) + P\Delta V. \] Solving for \(q\), we find: \[ q = w - P\Delta V. \] This indicates that when the enthalpy change is 0 during a constant-pressure process, the heat exchanged between the system and its surroundings (\(q\)) is equal to the difference between the work done by the gas on its surroundings (\(w\)) and the pressure-volume work done (\(P\Delta V\)).

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Most popular questions from this chapter

Consider the decomposition of liquid benzene, \(\mathrm{C}_{6} \mathrm{H}_{6}(l),\) to gaseous acetylene, \(\mathrm{C}_{2} \mathrm{H}_{2}(g) :\) $$\mathrm{C}_{6} \mathrm{H}_{6}(l) \longrightarrow 3 \mathrm{C}_{2} \mathrm{H}_{2}(g) \quad \Delta H=+630 \mathrm{kJ}$$ (a) What is the enthalpy change for the reverse reaction? (b) What is \(\Delta H\) for the formation of 1 mol of acetylene? (c) Which is more likely to be thermodynamically favored, the forward reaction or the reverse reaction? (d) If \(\mathrm{C}_{6} \mathrm{H}_{6}(g)\) were consumed instead of \(\mathrm{C}_{6} \mathrm{H}_{6}(l),\) would you expect the magnitude of \(\Delta H\) to increase, decrease, or stay the same? Explain.

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 cooled by removing 0.655 \(\mathrm{kJ}\) of heat. It shrinks on cooling, and the atmosphere does 382 J of work on the balloon. (b) A 100.0 -g bar of gold is heated from \(25^{\circ} \mathrm{C}\) to \(50^{\circ} \mathrm{C}\) during which it absorbs 322 \(\mathrm{J}\) of heat. Assume the volume of the gold bar remains constant.

(a) Write an equation that expresses the first law of thermodynamics in terms of heat and work. (b) Under what conditions will the quantities q and w be negative numbers?

For each of the following compounds, write a balanced thermochemical equation depicting the formation of one mole of the compound from its elements in their standard states and then look up \(\Delta H^{\circ} f\) for each substance in Appendix C. (a) \(\mathrm{NO}_{2}(g),(\mathbf{b}) \mathrm{SO}_{3}(g),(\mathbf{c}) \mathrm{NaBr}(s),(\mathbf{d}) \mathrm{Pb}\left(\mathrm{NO}_{3}\right)_{2}(s) .\)

Ammonia \(\left(\mathrm{NH}_{3}\right)\) boils at \(-33^{\circ} \mathrm{C} ;\) at this temperature it has a density of 0.81 \(\mathrm{g} / \mathrm{cm}^{3} .\) The enthalpy of formation of \(\mathrm{NH}_{3}(g)\) is \(-46.2 \mathrm{kJ} / \mathrm{mol},\) and the enthalpy of vaporization of \(\mathrm{NH}_{3}(l)\) is 23.2 \(\mathrm{kJ} / \mathrm{mol} .\) Calculate the enthalpy change when 1 \(\mathrm{L}\) of liquid \(\mathrm{NH}_{3}\) is burned in air to give \(\mathrm{N}_{2}(g)\) and \(\mathrm{H}_{2} \mathrm{O}(g) .\) How does this compare with \(\Delta H\) for the complete combustion of 1 Lof liquid methanol, \(\mathrm{CH}_{3} \mathrm{OH}(l) ?\) For \(\mathrm{CH}_{3} \mathrm{OH}(l),\) the density at \(25^{\circ} \mathrm{C}\) is \(0.792 \mathrm{g} / \mathrm{cm}^{3},\) and \(\Delta \mathrm{H}_{f}^{\circ}=-239 \mathrm{kJ} / \mathrm{mol}\)
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