Problem 82 - Chemistry and Chemical Reactivity

Question

The reaction of \(750 .\) g each of \(\mathrm{NH}_{3}\) and \(\mathrm{O}_{2}\) was found to produce \(562 \mathrm{g}\) of \(\mathrm{NO}\) (see pages \(161-162\) ). \(4 \mathrm{NH}_{3}(\mathrm{g})+5 \mathrm{O}_{2}(\mathrm{g}) \rightarrow 4 \mathrm{NO}(\mathrm{g})+6 \mathrm{H}_{2} \mathrm{O}(\ell)\) (a) What mass of water is produced by this reaction? (b) What mass of \(\mathrm{O}_{2}\) is required to consume \(750 . \mathrm{g}\) of \(\mathrm{NH}_{3} ?\)

Step-by-Step Solution

Answer

Molar masses calculated to find moles of reactants.

Step 1: Calculate the Moles of Reactants and Products

First, find the molar mass of each reactant and product. The molar mass of \(\mathrm{NH}_{3}\) is 17.03 g/mol, \(\mathrm{O}_{2}\) is 32.00 g/mol, \(\mathrm{NO}\) is 30.01 g/mol, and \(\mathrm{H}_{2}\mathrm{O}\) is 18.02 g/mol. Calculate the moles: \(750 \,\text{g} \div 17.03 \,\text{g/mol} = 44.05 \,\text{mol NH}_{3}\), and \(750 \,\text{g} \div 32.00 \,\text{g/mol} = 23.44 \,\text{mol O}_{2}\).

Key Concepts

Chemical Reactions

Understanding chemical reactions involves knowing how substances interact to form new products. Reactions can be represented through balanced chemical equations, which use symbols to show component substances and their quantities. For instance, the reaction we're looking at can be written as: \[4 \text{NH}_3(g) + 5 \text{O}_2(g) \rightarrow 4 \text{NO}(g) + 6 \text{H}_2\text{O}(l)\]This equation tells us that four molecules of ammonia (NH extsubscript{3}) react with five molecules of oxygen (O extsubscript{2}) to produce four molecules of nitrogen monoxide (NO) and six molecules of water (H extsubscript{2}O). Each term in the equation also follows the conservation of mass, where the mass of the reactants equals the mass of the products.

Molar Mass

Molar mass is a key concept in stoichiometry. It refers to the mass of one mole of a substance, expressed in grams per mole. To perform stoichiometric calculations like the ones in the exercise, knowing how to find molar mass is crucial. For example: - Ammonia (NH extsubscript{3}) has a molar mass of 17.03 g/mol. This is calculated by adding the molar masses of nitrogen (approximately 14.01 g/mol) and hydrogen (approximately 1.01 g/mol per atom times three). - Oxygen ( ext{O} extsubscript{2}) has a molar mass of 32.00 g/mol since it is made up of two oxygen atoms, each with a molar mass of 16.00 g/mol. - Nitrogen monoxide (NO) has a molar mass of 30.01 g/mol. - Water (H extsubscript{2}O) has a molar mass of 18.02 g/mol. Using these molar masses, you can convert between grams of a substance and moles, which is an essential step in many chemical calculations.

Limiting Reactants

Limiting reactants determine how much product can be formed in a chemical reaction. In every reaction, the reactants are consumed at different rates based on their balanced chemical equation. The limiting reactant is consumed first, stopping the reaction from continuing. To identify the limiting reactant in this exercise, compare the mole ratio from the balanced equation with the moles present: - From the equation, 4 moles of NH extsubscript{3} react with 5 moles of O extsubscript{2}. - We've calculated there are 44.05 moles of NH extsubscript{3} and 23.44 moles of O extsubscript{2}. By comparing the mole ratios, you can see that oxygen is the limiting reactant because it will run out before ammonia, which has excess.

Mass Calculations

Mass calculations allow us to determine how much product can be obtained from given reactants, considering the reaction's stoichiometry. Let's look at the calculations needed in this exercise:To find the mass of water produced:1. Identify the limiting reactant, which is O extsubscript{2} in this case.2. Use the stoichiometry of the reaction. For every 5 moles of O extsubscript{2}, 6 moles of H extsubscript{2}O are produced.3. Calculate moles of H extsubscript{2}O:\[23.44 \text{ moles O}_2 \times \frac{6 \text{ moles H}_2\text{O}}{5 \text{ moles O}_2} = 28.13 \text{ moles H}_2\text{O}\]4. Convert moles of H extsubscript{2}O to grams:\[28.13 \text{ moles H}_2\text{O} \times 18.02 \text{ g/mol} = 506.70 \text{ g H}_2\text{O}\]Through these calculations, you can find the amount of water produced given the starting amounts of reactants.