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Chapter 7: Problem 104

A calorimeter that measures an exothermic heat of reaction by the quantity of ice that can be melted is called an ice calorimeter. Now consider that \(0.100 \mathrm{L}\) of methane gas, \(\mathrm{CH}_{4}(\mathrm{g}),\) at \(25.0^{\circ} \mathrm{C}\) and \(744 \mathrm{mm} \mathrm{Hg}\) is burned at constant pressure in air. The heat liberated is captured and used to melt \(9.53 \mathrm{g}\) ice at \(0^{\circ} \mathrm{C}\left(\Delta H_{\text {fusion }} \text { of ice }=6.01 \mathrm{kJ} / \mathrm{mol}\right)\) (a) Write an equation for the complete combustion of \(\mathrm{CH}_{4},\) and show that combustion is incomplete in this case. (b) Assume that \(\mathrm{CO}(\mathrm{g})\) is produced in the incomplete combustion of \(\mathrm{CH}_{4}\), and represent the combustion as best you can through a single equation with small whole numbers as coefficients. \((\mathrm{H}_{2} \mathrm{O}(\mathrm{l})\) is another . product of the combustion.)

Short Answer

Expert verified
Part (a): The full combustion of methane is represented by the reaction \(CH₄(g) + 2O₂(g) -> CO₂(g) + 2H₂O(l)\). This combustion is incomplete in this case as less heat was released than the full combustion would typically liberate. Part (b): The incomplete combustion of methane, resulting in the production of carbon monoxide and water, can be represented by the equation \(CH₄(g) + 1.5O₂(g) -> CO(g) + 2H₂O(l)\).

Step by step solution

01

Part (a): Writing the full combustion of methane

The full combustion reaction of methane (CH₄) in the presence of oxygen (O₂) produces carbon dioxide (CO₂) and water (H₂O). This can be written as: \[CH₄(g) + 2O₂(g) -> CO₂(g) + 2H₂O(l)\]
02

Part (a): Analyzing incompleteness of the combustion

The fact that the heat released from the reaction was only enough to melt 9.53g of ice (equivalent to approx. 0.53 mol considering the fusion heat of ice) suggests that the combustion was incomplete - as the full combustion of one mole of methane typically releases more energy.
03

Part (b): Representing the incomplete combustion

When combustion is incomplete due to the insufficient supply of oxygen, carbon monoxide (CO) is produced instead of carbon dioxide. Keeping this in mind, and considering that water is also produced, the combustion can be represented by: \[CH₄(g) + 1.5O₂(g) -> CO(g) + 2H₂O(l)\] This equation assumes that for every mole of methane, one mole of carbon monoxide and two of water are produced, consuming 1.5 moles of oxygen in the process. The coefficients in this equation are all small whole numbers, as requested.

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Most popular questions from this chapter

Calculate the final temperature that results when (a) a 12.6 g sample of water at \(22.9^{\circ} \mathrm{C}\) absorbs \(875 \mathrm{J}\) of heat; (b) a 1.59 kg sample of platinum at \(78.2^{\circ} \mathrm{C}\) gives off \(1.05 \mathrm{kcal}\) of heat \(\left(\mathrm{sp} \mathrm{ht} \text { of } \mathrm{Pt}=0.032 \mathrm{cal} \mathrm{g}^{-1}\right.\) \(\left.^{\circ} \mathrm{C}^{-1}\right)\).

A 75.0 g piece of \(\mathrm{Ag}\) metal is heated to \(80.0^{\circ} \mathrm{C}\) and dropped into \(50.0 \mathrm{g}\) of water at \(23.2^{\circ} \mathrm{C} .\) The final temperature of the \(\mathrm{Ag}-\mathrm{H}_{2} \mathrm{O}\) mixture is \(27.6^{\circ} \mathrm{C}\). What is the specific heat of silver?

Thermite mixtures are used for certain types of welding, and the thermite reaction is highly exothermic. $$\begin{array}{r} \mathrm{Fe}_{2} \mathrm{O}_{3}(\mathrm{s})+2 \mathrm{Al}(\mathrm{s}) \longrightarrow \mathrm{Al}_{2} \mathrm{O}_{3}(\mathrm{s})+2 \mathrm{Fe}(\mathrm{s}) \\ \Delta H^{\circ}=-852 \mathrm{kJ} \end{array}$$ \(1.00 \mathrm{mol}\) of granular \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) and \(2.00 \mathrm{mol}\) of granular Al are mixed at room temperature \(\left(25^{\circ} \mathrm{C}\right),\) and a reaction is initiated. The liberated heat is retained within the products, whose combined specific heat over a broad temperature range is about \(0.8 \mathrm{Jg}^{-1}\) \(^{\circ} \mathrm{C}^{-1} .\) (The melting point of iron is \(1530^{\circ} \mathrm{C} .\) ) Show that the quantity of heat liberated is more than sufficient to raise the temperature of the products to the melting point of iron.

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 \(50.0^{\circ} \mathrm{C} ?\left[\Delta H_{\text {fusion }}^{\circ}=6.01 \mathrm{kJ} / \mathrm{mol}\right.\) \(\left.\mathrm{H}_{2} \mathrm{O}(\mathrm{s})\right]\)

A handbook lists two different values for the heat of combustion of hydrogen: \(33.88 \mathrm{kcal} / \mathrm{g} \mathrm{H}_{2}\) if \(\mathrm{H}_{2} \mathrm{O}(\mathrm{l})\) is formed, and \(28.67 \mathrm{kcal} / \mathrm{g} \mathrm{H}_{2}\) if \(\mathrm{H}_{2} \mathrm{O}(\mathrm{g})\) is formed. Explain why these two values are different, and indicate what property this difference represents. Devise a means of verifying your conclusions.
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