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Chapter 5: Problem 30

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.

Short Answer

Expert verified
The processes (a) change in potential energy when transferring a book from table to shelf and (b) heat evolved when a cube of sugar is oxidized are independent of the path by which the change occurs, as their outcomes depend only on the initial and final states. In contrast, (c) work accomplished in burning a gallon of gasoline is not independent of the path, as it depends on various factors such as engine efficiency and the combustion process.

Step by step solution

01

Process (a): Change in potential energy

The change in potential energy is calculated as the difference between the potential energy at the final position (shelf) and the potential energy at the initial position (table). This depends only on the height difference, the mass of the book, and the gravitational constant. No matter which path the book takes from the table to the shelf, this value will be the same. Therefore, the change in potential energy when transferring a book from table to shelf is independent of the path by which the change occurs.
02

Process (b): Heat evolved during sugar oxidation

The heat evolved during the oxidation of sugar is released due to the chemical reaction of sugar with oxygen and the formation of CO2 and H2O. The heat released in this reaction is determined by the changes in the chemical bonds within the molecules and does not depend on how the reaction occurs (i.e., the pathway through which sugar is oxidized). This means that the heat evolved during sugar oxidation is independent of the path by which the change occurs.
03

Process (c): Work accomplished in burning a gallon of gasoline

The work accomplished in burning a gallon of gasoline involves converting the chemical energy stored in gasoline into mechanical work. The amount of work done depends on various factors such as efficiency of the engine, the specific combustion process, and other external factors. This usually means that the amount of work accomplished can vary based on the path through which the gasoline is burned. As a result, the work accomplished in burning a gallon of gasoline is not independent of the path by which the change occurs. So, among the given processes, only (a) change in potential energy when transferring a book from table to shelf and (b) heat evolved when a cube of sugar is oxidized are independent of the path by which the change occurs.

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Most popular questions from this chapter

A 2.20-g sample of phenol $\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{OH}\right)$ was burned in a bomb calorimeter whose total heat capacity is \(11.90 \mathrm{~kJ} /{ }^{\circ} \mathrm{C} .\) The temperature of the calorimeter plus contents increased from 21.50 to $27.50^{\circ} \mathrm{C} .(\mathbf{a})$ Write a balanced chemical equation for the bomb calorimeter reaction. (b) What is the heat of combustion per gram of phenol and per mole of phenol?

It is estimated that the net amount of carbon dioxide fixed by photosynthesis on the landmass of Earth is \(5.5 \times 10^{16} \mathrm{~g} / \mathrm{yr}\) of \(\mathrm{CO}_{2}\). Assume that all this carbon is converted into glucose. (a) Calculate the energy stored by photosynthesis on land per year, in kJ. (b) Calculate the average rate of conversion of solar energy into plant energy in megawatts, MW \((1 \mathrm{~W}=1 \mathrm{~J} / \mathrm{s}) .\) A large nuclear power plant produces about \(10^{3} \mathrm{MW}\). The energy of how many such nuclear power plants is equivalent to the solar energy conversion?

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

When an 18.6-g sample of solid potassium hydroxide dissolves in $200.0 \mathrm{~g}$ of water in a coffee-cup calorimeter (Figure 5.18), the temperature rises from 23.7 to \(44.5^{\circ} \mathrm{C}\). (a) Calculate the quantity of heat (in kJ) released in the reaction. (b) Using your result from part (a), calculate \(\Delta H\) (in kJ/mol KOH) for the solution process. Assume that the specific heat of the solution is the same as that of pure water.

The complete combustion of methane, \(\mathrm{CH}_{4}(g)\), to form \(\mathrm{H}_{2} \mathrm{O}(l)\) and \(\mathrm{CO}_{2}(g)\) at constant pressure releases \(890 \mathrm{~kJ}\) of heat per mole of \(\mathrm{CH}_{4}\). (a) Write a balanced thermochemical equation for this reaction. (b) Draw an enthalpy diagram for the reaction.
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