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Chapter 7: Problem 15

The enthalpy change for the reaction $$\mathrm{CH}_{4}(g)+2 \mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(l)$$ is \(-891 \mathrm{kJ}\) for the reaction \(a s\) written. a. What quantity of heat is released for each mole of water formed? b. What quantity of heat is released for each mole of oxygen reacted?

Short Answer

Expert verified
a. The heat released per mole of water (\(\mathrm{H}_{2}\mathrm{O}\)) formed is \(445.5\, \text{kJ/mol}\). b. The heat released per mole of oxygen (\(\mathrm{O}_{2}\)) reacted is \(445.5\, \text{kJ/mol}\).

Step by step solution

01

Identify the Givens

In the given balanced reaction: \(\mathrm{CH}_{4}(g)+2 \mathrm{O}_{2}(g)\longrightarrow \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(l)\), the enthalpy change is \(-891 \mathrm{kJ}\). We need to determine the heat released per mole: a. For water (\(\mathrm{H}_{2}\mathrm{O}\)) b. For oxygen (\(\mathrm{O}_{2}\))
02

Calculate Heat Released per Mole of Water

First, we'll find the heat released per mole of water. According to the balanced reaction, 1 mole of \(\mathrm{CH}_{4}\) reacts with 2 moles of \(\mathrm{O}_{2}\) to form 2 moles of \(\mathrm{H}_{2}\mathrm{O}\). So, the heat released by the formation of 1 mole of water can be found using the given enthalpy change. \[\text{Heat released per mole of water} = \frac{-891\, \text{kJ}}{2\,\text{moles of }\mathrm{H}_{2}\mathrm{O}}\]
03

Solve for Heat Released per Mole of Water

Solve the expression to find the heat released per mole of water: \[\frac{-891\, \text{kJ}}{2 \text{ moles}} = -445.5\, \text{kJ/mol}\] Thus, \(445.5\, \text{kJ}\) of heat is released for each mole of water formed.
04

Calculate Heat Released per Mole of Oxygen

Now, we'll find the heat released per mole of oxygen. According to the balanced reaction, 1 mole of \(\mathrm{CH}_{4}\) reacts with 2 moles of \(\mathrm{O}_{2}\) to release the given heat. So, the heat released by the reaction of 1 mole of oxygen can also be found using the given enthalpy change. \[\text{Heat released per mole of oxygen} = \frac{-891\, \text{kJ}}{2\,\text{moles of }\mathrm{O}_{2}}\]
05

Solve for Heat Released per Mole of Oxygen

Solve the expression to find the heat released per mole of oxygen: \[\frac{-891\, \text{kJ}}{2 \text{ moles}} = -445.5\, \text{kJ/mol}\] Thus, \(445.5\, \text{kJ}\) of heat is released for each mole of oxygen reacted.
06

Answers

a. The heat released per mole of water (\(\mathrm{H}_{2}\mathrm{O}\)) formed is \(445.5\, \text{kJ/mol}\). b. The heat released per mole of oxygen (\(\mathrm{O}_{2}\)) reacted is \(445.5\, \text{kJ/mol}\).

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Most popular questions from this chapter

The reaction $$\mathrm{SO}_{3}(g)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{H}_{2} \mathrm{SO}_{4}(a q) $$ is the last step in the commercial production of sulfuric acid. The enthalpy change for this reaction is \(-227 \mathrm{kJ}\). In designing a sulfuric acid plant, is it necessary to provide for heating or cooling of the reaction mixture? Explain.

The enthalpy of combustion of \(\mathrm{CH}_{4}(g)\) when \(\mathrm{H}_{2} \mathrm{O}(l)\) is formed is \(-891 \mathrm{kJ} / \mathrm{mol}\) and the enthalpy of combustion of \(\mathrm{CH}_{4}(g)\) when \(\mathrm{H}_{2} \mathrm{O}(g)\) is formed is \(-803 \mathrm{kJ} / \mathrm{mol} .\) Use these data and Hess's law to determine the enthalpy of vaporization for water.

Hess's law is really just another statement of the first law of thermodynamics. Explain.

Consider the following equations: $$\begin{aligned}3 \mathrm{A}+6 \mathrm{B} \longrightarrow 3 \mathrm{D} & & \Delta H=-403 \mathrm{kJ} / \mathrm{mol} \\\\\mathrm{E}+2 \mathrm{F} \longrightarrow \mathrm{A} & & \Delta H=-105.2 \mathrm{kJ} / \mathrm{mol} \\\\\mathrm{C} \longrightarrow \mathrm{E}+3 \mathrm{D} & & \Delta H=64.8 \mathrm{kJ} / \mathrm{mol}\end{aligned}$$ Suppose the first equation is reversed and multiplied by \(\frac{1}{6},\) the second and third equations are divided by \(2,\) and the three adjusted equations are added. What is the net reaction and what is the overall heat of this reaction?

Why is it a good idea to rinse your thermos bottle with hot water before filling it with hot coffee?
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