Question

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

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

Step-by-step solution

- 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: \(\text {\Delta n_{\text {gas}}} = \text{moles of gaseous products} - \text{moles of gaseous reactants}\).

- 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, \(\text {\Delta n_{\text {gas}}} = 1 - 0 = 1\).

- 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, \(\text {\Delta n_{\text {gas}}} = 0 - 3 = -3\).

- 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, \(\text {\Delta n_{\text {gas}}} = 2 - 1 = 1\).

Key concepts

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.