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Chapter 17: Problem 29

Determine \(\Delta n_{\text {gas }}\) for each of the following reactions: (a) \(\mathrm{MgCO}_{3}(s) \rightleftharpoons \mathrm{MgO}(s)+\mathrm{CO}_{2}(g)\) (b) \(2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{H}_{2} \mathrm{O}(l)\) (c) \(\mathrm{HNO}_{3}(l)+\mathrm{ClF}(g) \rightleftharpoons \mathrm{ClONO}_{2}(g)+\mathrm{HF}(g)\)

Short Answer

Expert verified
(a) 1, (b) -3, (c) 1

Step by step solution

01

- Understanding \(\text {\Delta n_{\text {gas}}}\)

\(\text {\Delta n_{\text {gas}}}\) represents the change in the number of moles of gaseous reactants and products. It is calculated using the formula: \(\text {\Delta n_{\text {gas}}} = \text{moles of gaseous products} - \text{moles of gaseous reactants}\).
02

- Calculate \(\text {\Delta n_{\text {gas}}}\) for reaction (a)

For the reaction \(\mathrm{MgCO}_{3}(s) \rightleftharpoons \mathrm{MgO}(s) + \mathrm{CO}_{2}(g)\): \The gaseous products: 1 mole of \(\text{CO}_2\)\The gaseous reactants: 0 moles\Thus, \(\text {\Delta n_{\text {gas}}} = 1 - 0 = 1\).
03

- Calculate \(\text {\Delta n_{\text {gas}}}\) for reaction (b)

For the reaction \(2 \mathrm{H}_{2}(g) + \mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{H}_{2}\mathrm{O}(l)\): \The gaseous products: 0 moles\The gaseous reactants: 3 moles (2 moles of \(\mathrm{H}_2\) and 1 mole of \(\mathrm{O}_2\))\Thus, \(\text {\Delta n_{\text {gas}}} = 0 - 3 = -3\).
04

- Calculate \(\text {\Delta n_{\text {gas}}}\) for reaction (c)

For the reaction \(\mathrm{HNO}_{3}(l) + \mathrm{ClF}(g) \rightleftharpoons \mathrm{ClONO}_{2}(g) + \mathrm{HF}(g)\): \The gaseous products: 2 moles (1 mole of \(\mathrm{ClONO}_2\) and 1 mole of \(\mathrm{HF}\))\The gaseous reactants: 1 mole of \(\mathrm{ClF}\)\Thus, \(\text {\Delta n_{\text {gas}}} = 2 - 1 = 1\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Delta n_gas
Understanding the concept of \( \Delta n_{\text {gas}} \) is crucial in chemical reactions involving gases. It represents the change in the number of moles of gas during the reaction. It's calculated using the formula: \( \Delta n_{\text {gas}} = \text{moles of gaseous products} - \text{moles of gaseous reactants} \). This value helps you understand how the amount of gas changes as reactants turn into products. For instance, if a reaction starts with 2 moles of gas and ends with 4 moles of gas, the \( \Delta n_{\text {gas}} \) would be 2 (since 4 - 2 = 2). Conversely, if a reaction starts with more gas moles than it ends with, \( \Delta n_{\text {gas}} \) would be negative.
Stoichiometry
Stoichiometry is the study of the quantitative relationships between reactants and products in a chemical reaction. It involves using balanced chemical equations to determine the proportions of reactants and products. When you're dealing with gases, stoichiometry can help you find out the volumes and numbers of moles involved. This is essential for calculating \( \Delta n_{\text {gas}} \), as it informs you of the exact mole quantities of gases before and after the reaction. Remember, the coefficients in a balanced chemical equation represent the ratios in which substances react or are produced.
Chemical Reactions
Chemical reactions involve the transformation of reactants into products. These processes can change the state and amount of matter involved. When gases are part of the reaction, their moles need to be carefully tracked. By observing the balanced equation of a reaction, you can determine which substances are gases and their respective amounts. This is important when calculating \( \Delta n_{\text {gas}} \). For example, in the reaction \( 2 \mathrm{H}_{2}(g) + \mathrm{O}_{2}(g) \rightarrow 2 \mathrm{H}_{2}\mathrm{O}(l) \), there is a reduction in gas moles, indicating that \( \Delta n_{\text {gas}} = -3 \).
Moles of Gas
Understanding moles of gas is fundamental in interpreting chemical reactions. A mole is a basic unit in chemistry representing \( 6.022 \times 10^{23} \) particles of a given substance. In the context of gases, the mole concept is used to express volumes under standard conditions. When you calculate \( \Delta n_{\text {gas}} \), you focus on how many moles of gas there are before and after a reaction. For a reaction, if one mole of \( \mathrm{CO}_2 \) gas is produced from a solid \( \mathrm{MgCO}_3 \), \( \Delta n_{\text {gas}} \) would be +1, showing an increase in moles of gas.

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Most popular questions from this chapter

Consider the formation of ammonia in two experiments. (a) To a 1.00 -L container at \(727^{\circ} \mathrm{C}, 1.30 \mathrm{~mol}\) of \(\mathrm{N}_{2}\) and \(1.65 \mathrm{~mol}\) of \(\mathrm{H}_{2}\) are added. At equilibrium, \(0.100 \mathrm{~mol}\) of \(\mathrm{NH}_{3}\) is present. Calculate the equilibrium concentrations of \(\mathrm{N}_{2}\) and \(\mathrm{H}_{2}\), and find \(K_{\mathrm{c}}\) for the reaction $$ 2 \mathrm{NH}_{3}(g) \rightleftharpoons \mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) $$ (b) In a different 1.00 -L container at the same temperature, equilibrium is established with \(8.34 \times 10^{-2} \mathrm{~mol}\) of \(\mathrm{NH}_{3}, 1.50 \mathrm{~mol}\) of \(\mathrm{N}_{2}\) and \(1.25 \mathrm{~mol}\) of \(\mathrm{H}_{2}\) present. Calculate \(K_{\mathrm{c}}\) for the reaction $$ \mathrm{NH}_{3}(g) \rightleftharpoons \frac{1}{2} \mathrm{~N}_{2}(g)+\frac{3}{2} \mathrm{H}_{2}(g) $$ (c) What is the relationship between the \(K_{\mathrm{c}}\) values in parts (a) and (b)? Why aren't these values the same?

In the \(1980 \mathrm{~s}, \mathrm{CFC}-11\) was one of the most heavily produced chlorofluorocarbons. The last step in its formation is $$ \mathrm{CCl}_{4}(g)+\mathrm{HF}(g) \rightleftharpoons \mathrm{CFCl}_{3}(g)+\mathrm{HCl}(g) $$ If you start the reaction with equal concentrations of \(\mathrm{CCl}_{4}\) and \(\mathrm{HF}\), you obtain equal concentrations of \(\mathrm{CFCl}_{3}\) and \(\mathrm{HCl}\) at equilibrium. Are the final concentrations of \(\mathrm{CFCl}_{3}\) and \(\mathrm{HCl}\) equal if you start with unequal concentrations of \(\mathrm{CCl}_{4}\) and HF? Explain.

In a study of the thermal decomposition of lithium peroxide, $$ 2 \mathrm{Li}_{2} \mathrm{O}_{2}(s) \rightleftharpoons 2 \mathrm{Li}_{2} \mathrm{O}(s)+\mathrm{O}_{2}(g) $$ a chemist finds that, as long as some \(\mathrm{Li}_{2} \mathrm{O}_{2}\) is present at the end of the experiment, the amount of \(\mathrm{O}_{2}\) obtained in a given container at a given \(T\) is the same. Explain.

As an EPA scientist studying catalytic converters and urban smog, you want to find \(K_{c}\) for the following reaction: $$ 2 \mathrm{NO}_{2}(g) \rightleftharpoons \mathrm{N}_{2}(g)+2 \mathrm{O}_{2}(g) \quad K_{\mathrm{c}}=? $$ Use the following data to find the unknown \(K_{\mathrm{c}}\) : $$ \begin{aligned} \frac{1}{2} \mathrm{~N}_{2}(g)+\frac{1}{2} \mathrm{O}_{2}(g) & \rightleftharpoons \mathrm{NO}(g) & & K_{\mathrm{c}}=4.8 \times 10^{-10} \\ 2 \mathrm{NO}_{2}(g) & \Longrightarrow 2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) & & K_{\mathrm{c}}=1.1 \times 10^{-5} \end{aligned} $$

The following reaction can be used to make \(\mathrm{H}_{2}\) for the synthesis of ammonia from the greenhouse gases carbon dioxide and methane: $$ \mathrm{CH}_{4}(g)+\mathrm{CO}_{2}(g) \rightleftharpoons 2 \mathrm{CO}(g)+2 \mathrm{H}_{2}(g) $$ (a) What is the percent yield of \(\mathrm{H}_{2}\) when an equimolar mixture of \(\mathrm{CH}_{4}\) and \(\mathrm{CO}_{2}\) with a total pressure of 20.0 atm reaches equilibrium at \(1200 . \mathrm{K},\) at which \(K_{\mathrm{p}}=3.548 \times 10^{6} ?\) (b) What is the percent yield of \(\mathrm{H}_{2}\) for this system at \(1300 . \mathrm{K},\) at which \(K_{\mathrm{p}}=2.626 \times 10^{7} ?\) (c) Use the van't Hoff equation to find \(\Delta H_{\mathrm{rnn}}^{\circ}\)
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