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Chapter 5: Problem 25

Calculate \(\Delta E\) and determine whether the process is endothermic or exothermic for the following cases: \((\mathbf{a}) q=0.763 \mathrm{~kJ}\) and \(w=-840 \mathrm{~J}\). (b) A system releases \(66.1 \mathrm{~kJ}\) of heat to its surroundings while the surroundings do \(44.0 \mathrm{~kJ}\) of work on the system.

Short Answer

Expert verified
In case (a): ΔE = -0.077 kJ, making the process exothermic. In case (b): ΔE = -22.1 kJ, also making the process exothermic.

Step by step solution

01

Calculate ΔE using ΔE = q + w

For this case, we're given values for q and w. We just need to plug these values into the equation: ΔE = q + w. Note that q and w have different units, so we need to make sure they have the same units before addition. w is given in Joules (J), while q is given in kilojoules (kJ). We can convert w to kJ by dividing it by 1000. So, ΔE = (0.763 kJ) + (-840 J * 1 kJ/1000 J) ΔE = 0.763 kJ - 0.84 kJ
02

Determine whether the process is endothermic or exothermic

Now that the units are the same, we can calculate ΔE: ΔE = -0.077 kJ Since ΔE is negative, the process is exothermic. Case (b):
03

Determine the signs of q and w

We're given that the system releases 66.1 kJ of heat to its surroundings, which means q = -66.1 kJ (heat released is negative). We're also given that the surroundings do 44.0 kJ of work on the system, which means w = +44.0 kJ (work done on the system is positive).
04

Calculate ΔE using ΔE = q + w

With the signs of q and w determined, we can calculate ΔE: ΔE = q + w ΔE = (-66.1 kJ) + (44.0 kJ)
05

Determine whether the process is endothermic or exothermic

Now we can calculate ΔE: ΔE = -22.1 kJ Since ΔE is negative, the process is exothermic.

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Most popular questions from this chapter

Three hydrocarbons that contain four carbons are listed here, along with their standard enthalpies of formation: $$ \begin{array}{llc} \hline \text { Hydrocarbon } & \text { Formula } & \Delta H_{f}^{0}(\mathrm{~kJ} / \mathrm{mol}) \\ \hline \text { Butane } & \mathrm{C}_{4} \mathrm{H}_{10}(g) & -125 \\ \text { 1-Butene } & \mathrm{C}_{4} \mathrm{H}_{8}(g) & -1 \\ \text { 1-Butyne } & \mathrm{C}_{4} \mathrm{H}_{6}(g) & 165 \\ \hline \end{array} $$ (a) For each of these substances, calculate the molar enthalpy of combustion to \(\mathrm{CO}_{2}(g)\) and \(\mathrm{H}_{2} \mathrm{O}(l)\) (b) Calculate the fuel value, in \(\mathrm{kJ} / \mathrm{g}\), for each of these compounds. (c) For each hydrocarbon, determine the percentage of hydrogen by mass. (d) By comparing your answers for parts (b) and (c), propose a relationship between hydrogen content and fuel value in hydrocarbons.

Without doing any calculations, predict the sign of \(\Delta H\) for each of the following reactions: (a) \(2 \mathrm{NO}_{2}(g) \longrightarrow \mathrm{N}_{2} \mathrm{O}_{4}(g)\) (b) \(2 \mathrm{~F}(g) \longrightarrow \mathrm{F}_{2}(g)\) (c) $\mathrm{Mg}^{2+}(g)+2 \mathrm{Cl}^{-}(g) \longrightarrow \mathrm{MgCl}_{2}(s)$ (d) \(\mathrm{HBr}(g) \longrightarrow \mathrm{H}(g)+\mathrm{Br}(g)\)

Write balanced equations that describe the formation of the following compounds from elements in their standard states, and then look up the standard enthalpy of formation for each substance in Appendix C: (a) \(\mathrm{CH}_{3} \mathrm{OH}(l),\) (b) \(\mathrm{CaSO}_{4}(s),\) (d) \(\mathrm{P}_{4} \mathrm{O}_{6}(s),\) (c) \(\mathrm{NO}(g)\).

Suppose that the gas-phase reaction $2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \longrightarrow\( \)2 \mathrm{NO}_{2}(g)$ were carried out in a constant-volume container at constant temperature. (a) Would the measured heat change represent \(\Delta H\) or \(\Delta E\) ? (b) If there is a difference, which quantity is larger for this reaction? (c) Explain your answer to part (b).

Indicate which of the following is independent of the path by which a change occurs: (a) the change in potential energy when a book is transferred from table to shelf, (b) the heat evolved when a cube of sugar is oxidized to \(\mathrm{CO}_{2}(g)\) and \(\mathrm{H}_{2} \mathrm{O}(g),(\mathbf{c})\) the work accomplished in burning a gallon of gasoline.
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