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Chapter 5: Problem 32

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 \(\mathrm{H}_{2} \mathrm{O}(g),\) (c) the work accomplished in burning a gallon of gasoline.

Short Answer

Expert verified
The change in potential energy when a book is transferred from table to shelf (a) and the heat evolved when a cube of sugar is oxidized to CO₂(g) and H₂O(g) (b) are independent of the path by which a change occurs. The work accomplished in burning a gallon of gasoline (c) is dependent on the path and not independent.

Step by step solution

01

A. Analyzing the change in potential energy

When a book is transferred from table to shelf, the change in potential energy is determined by the difference in heights between the table and the shelf. It is given by the equation ΔPE = m × g × Δh, where m is the mass of the book, g is the gravitational constant, and Δh is the difference in heights. In this case, the change in potential energy depends only on the initial and final heights and not on the path taken to transfer the book. Therefore, this process is independent of the path.
02

B. Analyzing the heat evolved during oxidation of sugar

When a cube of sugar is oxidized to CO₂(g) and H₂O(g), the heat evolved in this process, known as enthalpy change (ΔH), is a state function that depends only on the initial and final states of the system. It is independent of the path or mechanism by which the reaction occurs. Therefore, the heat evolved during the oxidation of sugar is independent of the path.
03

C. Analyzing the work accomplished in burning a gallon of gasoline

When a gallon of gasoline is burned, the work accomplished depends on various factors such as engine efficiency, driving conditions, and various other factors. The work accomplished is not solely dependent on the initial and final states of the gasoline, but also on how efficiently the energy in the gasoline is utilized during the process. Therefore, the work accomplished in burning a gallon of gasoline is dependent on the path and not independent. Conclusion:
04

Answer

Among the given processes, the change in potential energy when a book is transferred from table to shelf (a) and the heat evolved when a cube of sugar is oxidized to CO₂(g) and H₂O(g) (b) are independent of the path by which a change occurs. The work accomplished in burning a gallon of gasoline (c) is not independent of the path.

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Most popular questions from this chapter

Identify the force present and explain whether work is being performed in the following cases: (a) You lift a pencil off the top of a desk. (b) A spring is compressed to half its normal length.

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 mol of hydrogen atoms or \(1 \mathrm{~mol}\) of \(\mathrm{H}_{2},\) (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 \(25^{\circ} \mathrm{C},\) (d) \(1 \mathrm{~mol} \mathrm{~N}_{2}(g)\) at \(100{ }^{\circ} \mathrm{C}\) or \(1 \mathrm{~mol}\) \(\mathrm{N}_{2}(g)\) at \(300^{\circ} \mathrm{C}\)

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

Many portable gas heaters and grills use propane, \(\mathrm{C}_{3} \mathrm{H}_{8}(g),\) as a fuel. Using standard enthalpies of formation, calculate the quantity of heat produced when \(10.0 \mathrm{~g}\) of propane is completely combusted in air under standard conditions.

Using values from Appendix \(\mathrm{C},\) calculate the standard enthalpy change for each of the following reactions: (a) \(2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{SO}_{3}(g)\) (b) \(\mathrm{Mg}(\mathrm{OH})_{2}(s) \longrightarrow \mathrm{MgO}(s)+\mathrm{H}_{2} \mathrm{O}(l)\) (c) \(\mathrm{N}_{2} \mathrm{O}_{4}(g)+4 \mathrm{H}_{2}(g) \longrightarrow \mathrm{N}_{2}(g)+4 \mathrm{H}_{2} \mathrm{O}(g)\) (d) \(\mathrm{SiCl}_{4}(l)+2 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{SiO}_{2}(s)+4 \mathrm{HCl}(g)\)
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