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Chapter 5: Problem 26

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 \(382 \mathrm{~J}\) 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.

Short Answer

Expert verified
In summary: (a) The change in internal energy is \(-273 \mathrm{~J}\), and the process is exothermic. (b) The change in internal energy is \(322 \mathrm{~J}\), and the process is endothermic.

Step by step solution

01

Determine the heat (q) given to the system

We are given that 0.655 kJ of heat is removed from the system, which means q = -0.655 kJ. We need to convert this into J (joules) for consistency: \(q = -0.655 \times 1000 = -655 \mathrm{~J}\).
02

Determine the work (w) done on the system

We are given that the atmosphere does 382 J of work on the system, which means w = 382 J.
03

Calculate the change in internal energy (ΔU)

We can now use the formula to calculate the change in internal energy (ΔU). ΔU = q + w = (-655 J) + (382 J) = -273 J
04

Determine if the process is endothermic or exothermic

Since the change in internal energy (ΔU) is negative, the process is exothermic. The balloon loses energy to its surroundings as it cools. For case (b)...
05

Determine the heat (q) given to the system

We are given that the gold bar absorbs 322 J of heat, which means q = 322 J.
06

Determine the work (w) done on the system

Since the volume of the gold bar remains constant, there is no work done on the system. Therefore, w = 0 J.
07

Calculate the change in internal energy (ΔU)

We can now use the formula to calculate the change in internal energy (ΔU). ΔU = q + w = (322 J) + (0 J) = 322 J
08

Determine if the process is endothermic or exothermic

Since the change in internal energy (ΔU) is positive, the process is endothermic. The gold bar gains energy from its surroundings as it is heated. To summarize, the process in case (a) is exothermic, and the change in internal energy is -273 J. The process in case (b) is endothermic, and the change in internal energy is 322 J.

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Most popular questions from this chapter

At the end of 2012, global population was about 7.0 billion people. What mass of glucose in kg would be needed to provide 1500 Cal/person/day of nourishment to the global population for one year? Assume that glucose is metabolized entirely to \(\mathrm{CO}_{2}(g)\) and \(\mathrm{H}_{2} \mathrm{O}(l)\) according to the following thermochemical equation: $$ \begin{aligned} \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(s)+6 \mathrm{O}_{2}(g) \longrightarrow 6 \mathrm{CO}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(l) \\ \Delta H^{\circ} &=-2803 \mathrm{~kJ} \end{aligned} $$

Consider the combustion of liquid methanol, \(\mathrm{CH}_{3} \mathrm{OH}(l):\) $$ \begin{aligned} \mathrm{CH}_{3} \mathrm{OH}(l)+\frac{3}{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(l) & \\ \Delta H=&-726.5 \mathrm{~kJ} \end{aligned} $$ (a) What is the enthalpy change for the reverse reaction? (b) Balance the forward reaction with whole-number coefficients. What is \(\Delta H\) for the reaction represented by this equation? (c) Which is more likely to be thermodynamically favored, the forward reaction or the reverse reaction? (d) If the reaction were written to produce \(\mathrm{H}_{2} \mathrm{O}(g)\) instead of \(\mathrm{H}_{2} \mathrm{O}(l),\) would you expect the magnitude of \(\Delta H\) to increase, decrease, or stay the same? Explain.

When solutions containing silver ions and chloride ions are mixed, silver chloride precipitates $$ \mathrm{Ag}^{+}(a q)+\mathrm{Cl}^{-}(a q) \longrightarrow \operatorname{AgCl}(s) \quad \Delta H=-65.5 \mathrm{~kJ} $$ (a) Calculate \(\Delta H\) for the production of \(0.450 \mathrm{~mol}\) of \(\mathrm{AgCl}\) by this reaction. (b) Calculate \(\Delta H\) for the production of \(9.00 \mathrm{~g}\) of $\mathrm{AgCl} . (\mathbf{c})\( Calculate \)\Delta H\( when \)9.25 \times 10^{-4} \mathrm{~mol}$ of \(\mathrm{AgCl}\) dissolves in water.

(a) Why does the standard enthalpy of formation of both the very reactive fluorine \(\left(\mathrm{F}_{2}\right)\) and the almost inert gas nitrogen \(\left(\mathrm{N}_{2}\right)\) both read zero? (b) Write the chemical equation for the reaction whose enthalpy change is the standard enthalpy of formation of naphthalene \(\left(\mathrm{C}_{10} \mathrm{H}_{8}\right)\).

(a) Which releases the most energy when metabolized, \(1 \mathrm{~g}\) of carbohydrates or \(1 \mathrm{~g}\) of fat? (b) A particular chip snack food is composed of \(12 \%\) protein, \(14 \%\) fat, and the rest carbohydrate. What percentage of the calorie content of this food is fat? (c) How many grams of protein provide the same fuel value as \(25 \mathrm{~g}\) of fat?
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