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Chapter 5: Problem 42

Without referring to tables, predict which of the following has the higher enthalpy in each case: (a) 1 \(\mathrm{mol} \mathrm{CO}_{2}(s)\) or 1 \(\mathrm{mol} \mathrm{CO}_{2}(g)\) at the same temperature, ( b) 2 \(\mathrm{mol}\) of hydrogen atoms or 1 \(\mathrm{mol}\) of \(\mathrm{H}_{2},(\mathbf{c}) 1 \mathrm{mol} \mathrm{H}_{2}(g)\) and 0.5 \(\mathrm{mol} \mathrm{O}_{2}(g)\) at \(25^{\circ} \mathrm{C}\) or 1 \(\mathrm{mol} \mathrm{H}_{2} \mathrm{O}(g)\) at \(25^{\circ} \mathrm{C},(\mathbf{d}) 1 \mathrm{mol} \mathrm{N}_{2}(g)\) at \(100^{\circ} \mathrm{C}\) or 1 \(\mathrm{mol} \mathrm{N}_{2}(g)\) at \(300^{\circ} \mathrm{C}\) .

Short Answer

Expert verified
(a) 1 mol of CO₂(g) has higher enthalpy than 1 mol of CO₂(s). (b) 2 mol of hydrogen atoms have higher enthalpy than 1 mol of H₂. (c) 1 mol H₂(g) and 0.5 mol O₂(g) have higher enthalpy than 1 mol H₂O(g) at 25°C. (d) 1 mol of N₂(g) at 300°C has a higher enthalpy than 1 mol of N₂(g) at 100°C.

Step by step solution

01

Case (a): 1 mol CO₂(s) or 1 mol CO₂(g) at the same temperature

When comparing a solid and a gas at the same temperature, the gas usually has higher enthalpy. The reason is that, in the gas state, particles have higher kinetic energy due to their increased freedom of movement. Therefore, 1 mol of CO₂(g) has higher enthalpy than 1 mol of CO₂(s).
02

Case (b): 2 mol of hydrogen atoms or 1 mol of H₂

Here, we can consider the fact that a covalent bond exists in H₂, which requires energy to break. In other words, forming a bond in H₂ releases energy, making the molecule's enthalpy lower. Therefore, 2 mol of hydrogen atoms have higher enthalpy than 1 mol of H₂.
03

Case (c): 1 mol H₂(g) and 0.5 mol O₂(g) at 25°C or 1 mol H₂O(g) at 25°C

In this case, we can use enthalpy of formation concept. The enthalpy of formation of H₂O(g) is negative, meaning that its formation releases energy. Conversely, breaking the bonds in H₂O(g) requires energy. Therefore, 1 mol H₂(g) and 0.5 mol O₂(g) have higher enthalpy since they have not yet formed into H₂O(g).
04

Case (d): 1 mol N₂(g) at 100°C or 1 mol N₂(g) at 300°C

In this case, we are comparing the same substance at two different temperatures. The higher the temperature, the more kinetic energy and, consequently, enthalpy is possessed by the particles. Therefore, 1 mol of N₂(g) at 300°C has a higher enthalpy than 1 mol of N₂(g) at 100°C.

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Most popular questions from this chapter

Consider the following reaction: $$2 \mathrm{CH}_{3} \mathrm{OH}(g) \longrightarrow 2 \mathrm{CH}_{4}(g)+\mathrm{O}_{2}(g) \quad \Delta H=+252.8 \mathrm{kJ}$$ (a) Is this reaction exothermic or endothermic? (b) Calculate the amount of heat transferred when 24.0 of \(\mathrm{CH}_{3} \mathrm{OH}(g)\) is decomposed by this reaction at constant pressure. (c) For a given sample of \(\mathrm{CH}_{3} \mathrm{OH},\) the enthalpy change during the reaction is 82.1 kJ. How many grams of methane gas are produced? (\mathbf{d} ) How many kilojoules of heatare released when 38.5 \(\mathrm{g}\) of \(\mathrm{CH}_{4}(g)\) reacts completely with \(\mathrm{O}_{2}(g)\) to form \(\mathrm{CH}_{3} \mathrm{OH}(g)\) at constant pressure?

(a) A serving of a particular ready-to-serve chicken noodle soup contains 2.5 \(\mathrm{g}\) fat, 14 \(\mathrm{g}\) carbohydrate, and 7 \(\mathrm{g}\) protein. Estimate the number of Calories in a serving. (b) According to its nutrition label, the same soup also contains 690 \(\mathrm{mg}\) of sodium. Do you think the sodium contributes to the caloric content of the soup?

Identify the force present and explain whether work is done when (a) a positively charged particle moves in a circle at a fixed distance from a negatively charged particle, (b) an iron nail is pulled off a magnet.

(a) Which of the following cannot leave or enter a closed system: heat, work, or matter? (b) Which cannot leave or enter an isolated system? (c) What do we call the part of the universe that is not part of the system?

From the enthalpies of reaction $$\begin{aligned} 2 \mathrm{C}(s)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{CO}(g) & \Delta H=-221.0 \mathrm{kJ} \\ 2 \mathrm{C}(s)+\mathrm{O}_{2}(g)+4 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{CH}_{3} \mathrm{OH}(g) & \Delta H=-402.4 \mathrm{kJ} \end{aligned}$$ calculate \(\Delta H\) for the reaction $$\mathrm{CO}(g)+2 \mathrm{H}_{2}(g) \longrightarrow \mathrm{CH}_{3} \mathrm{OH}(g)$$
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