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Chapter 7: Problem 16

Upon complete combustion, the indicated substances evolve the given quantities of heat. Write a balanced equation for the combustion of \(1.00 \mathrm{mol}\) of each substance, including the enthalpy change, \(\Delta H\), for the reaction.Upon complete combustion, the indicated substances evolve the given quantities of heat. Write a balanced equation for the combustion of \(1.00 \mathrm{mol}\) of each substance, including the enthalpy change, \(\Delta H\), for the reaction. (a) \(0.584 \mathrm{g}\) of propane, \(\mathrm{C}_{3} \mathrm{H}_{8}(\mathrm{g}),\) yields \(29.4 \mathrm{kJ}\) (b) \(0.136 \mathrm{g}\) of camphor, \(\mathrm{C}_{10} \mathrm{H}_{16} \mathrm{O}(\mathrm{s}),\) yields \(5.27 \mathrm{kJ}\) (c) \(2.35 \mathrm{mL}\) of acetone, \(\left(\mathrm{CH}_{3}\right)_{2} \mathrm{CO}(\mathrm{l})(d=0.791\) \(\mathrm{g} / \mathrm{mL}),\) yields \(58.3 \mathrm{kJ}\)

Short Answer

Expert verified
\[ \mathrm{C}_{3} \mathrm{H}_{8}(g) + 5O_{2}(g) \rightarrow 3CO_{2}(g) + 4H_{2}O(l), \Delta H = -29.4 \mathrm{kJ}\] \[ \mathrm{C}_{10} \mathrm{H}_{16} \mathrm{O}(s) + 15O_{2}(g) \rightarrow 10CO_{2}(g) + 8H_{2}O(l) , \Delta H = -5.27 \mathrm{kJ}\] \[ \left(\mathrm{CH}_{3}\right)_{2} \mathrm{CO}(l) + 4O_{2}(g) \rightarrow 3CO_{2}(g) + 3H_{2}O(l) , \Delta H = -58.3 \mathrm{kJ}\]

Step by step solution

01

Combustion of propane

Balance the following equation: \(\mathrm{C}_{3} \mathrm{H}_{8}(g) + 5O_{2}(g) \rightarrow 3CO_{2}(g) + 4H_{2}O(l)\) and append the enthalpy change: \(\mathrm{C}_{3} \mathrm{H}_{8}(g) + 5O_{2}(g) \rightarrow 3CO_{2}(g) + 4H_{2}O(l) \quad \Delta H = -29.4 \mathrm{kJ}\)
02

Combustion of camphor

Balance the equation: \(\mathrm{C}_{10} \mathrm{H}_{16} \mathrm{O}(s) + 15O_{2}(g) \rightarrow 10CO_{2}(g) + 8H_{2}O(l)\) and append the enthalpy change: \(\mathrm{C}_{10} \mathrm{H}_{16} \mathrm{O}(s) + 15O_{2}(g) \rightarrow 10CO_{2}(g) + 8H_{2}O(l) \quad \Delta H = -5.27 \mathrm{kJ}\)
03

Combustion of acetone

Balance the equation: \(\left(\mathrm{CH}_{3}\right)_{2} \mathrm{CO}(l) + 4O_{2}(g) \rightarrow 3CO_{2}(g) + 3H_{2}O(l)\) and append the enthalpy change: \(\left(\mathrm{CH}_{3}\right)_{2} \mathrm{CO}(l) + 4O_{2}(g) \rightarrow 3CO_{2}(g) + 3H_{2}O(l) \quad \Delta H = -58.3 \mathrm{kJ}\)

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Most popular questions from this chapter

A \(7.26 \mathrm{kg}\) shot (as used in the sporting event, the shot put) is dropped from the top of a building \(168 \mathrm{m}\) high. What is the maximum temperature increase that could occur in the shot? Assume a specific heat of \(0.47 \mathrm{Jg}^{-1}\) \(^{\circ} \mathrm{C}^{-1}\) for the shot. Why would the actual measured temperature increase likely be less than the calculated value?

In the Are You Wondering \(7-1\) box, the temperature variation of enthalpy is discussed, and the equation \(q_{P}=\) heat capacity \(\times\) temperature change \(=C_{P} \times \Delta T\) was introduced to show how enthalpy changes with temperature for a constant-pressure process. Strictly speaking, the heat capacity of a substance at constant pressure is the slope of the line representing the variation of enthalpy (H) with temperature, that is $$C_{P}=\frac{d H}{d T} \quad(\text { at constant pressure })$$ where \(C_{P}\) is the heat capacity of the substance in question. Heat capacity is an extensive quantity and heat capacities are usually quoted as molar heat capacities \(C_{P, \mathrm{m}},\) the heat capacity of one mole of substance; an intensive property. The heat capacity at constant pressure is used to estimate the change in enthalpy due to a change in temperature. For infinitesimal changes in temperature, $$d H=C_{p} d T \quad(\text { at constant pressure })$$ To evaluate the change in enthalpy for a particular temperature change, from \(T_{1}\) to \(T_{2}\), we write $$\int_{H\left(T_{1}\right)}^{H\left(T_{2}\right)} d H=H\left(T_{2}\right)-H\left(T_{1}\right)=\int_{T_{1}}^{T_{2}} C_{P} d T$$ If we assume that \(C_{P}\) is independent of temperature, then we recover equation (7.5) $$\Delta H=C_{P} \times \Delta T$$ On the other hand, we often find that the heat capacity is a function of temperature; a convenient empirical expression is $$C_{P, \mathrm{m}}=a+b T+\frac{c}{T^{2}}$$ What is the change in molar enthalpy of \(\mathrm{N}_{2}\) when it is heated from \(25.0^{\circ} \mathrm{C}\) to \(100.0^{\circ} \mathrm{C} ?\) The molar heat capacity of nitrogen is given by$$C_{P, \mathrm{m}}=28.58+3.77 \times 10^{-3} T-\frac{0.5 \times 10^{5}}{T^{2}} \mathrm{JK}^{-1} \mathrm{mol}^{-1}$$

What mass of ice can be melted with the same quantity of heat as required to raise the temperature of \(3.50 \mathrm{mol} \mathrm{H}_{2} \mathrm{O}(1)\) by \(50.0^{\circ} \mathrm{C} ?\left[\Delta H_{\text {fusion }}^{\circ}=6.01 \mathrm{kJ} / \mathrm{mol}\right.\) \(\left.\mathrm{H}_{2} \mathrm{O}(\mathrm{s})\right]\)

Construct a concept map encompassing the ideas behind the first law of thermodynamics.

The internal energy of a fixed quantity of an ideal gas depends only on its temperature. A sample of an ideal gas is allowed to expand at a constant temperature (isothermal expansion). (a) Does the gas do work? (b) Does the gas exchange heat with its surroundings? (c) What happens to the temperature of the gas? (d) What is \(\Delta U\) for the gas?
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