Question

Gold metal will dissolve only in aqua regia, a mixture of concentrated hydrochloric acid and concentrated nitric acid in a 3: 1 volume ratio. The products of the reaction between gold and the concentrated acids are \(\mathrm{AuCl}_{4}^{-}(a q), \mathrm{NO}(g),\) and \(\mathrm{H}_{2} \mathrm{O}\). The equation for this reaction where \(\mathrm{HNO}_{3}\) and \(\mathrm{HCl}\) are strong acids is $$ \begin{aligned} \mathrm{Au}(s)+4 \mathrm{Cl}^{-}(a q)+4 \mathrm{H}^{+}(a q)+\mathrm{NO}_{3}^{-}(a q) & \longrightarrow \\ \mathrm{AuCl}_{4}^{-}(a q)+\mathrm{NO}(g)+2 \mathrm{H}_{2} \mathrm{O} \end{aligned} $$ (a) What stoichiometric ratio of hydrochloric acid to nitric acid should be used? (b) What volumes of \(12 \mathrm{M} \mathrm{HCl}\) and \(16 \mathrm{M} \mathrm{HNO}_{3}\) are required to furnish the \(\mathrm{Cl}^{-}\) and \(\mathrm{NO}_{3}^{-}\) ions to react with \(25.0 \mathrm{~g}\) of gold?

Short answer

Answer: The stoichiometric ratio of HCl to HNO3 for dissolving gold is 4:1. The volumes of 12 M HCl and 16 M HNO3 solutions needed to react with 25.0 g of gold are 0.0423 L and 0.00794 L, respectively.

Step-by-step solution

Determine the stoichiometric ratio of hydrochloric acid (HCl) to nitric acid (HNO3)

The reaction equation provided is: $$ \mathrm{Au}(s)+4 \mathrm{Cl}^{-}(a q)+4 \mathrm{H}^{+}(a q)+\mathrm{NO}_{3}^{-}(a q) \longrightarrow \mathrm{AuCl}_{4}^{-}(a q)+\mathrm{NO}(g)+2 \mathrm{H}_{2} \mathrm{O} $$ From the balanced equation, we can see that we need 4 moles of \(\mathrm{Cl}^-\) ions from HCl and 1 mole of \(\mathrm{NO}_3^-\) ion from HNO3. Therefore, the stoichiometric ratio of HCl to HNO3 is 4:1. (a) The stoichiometric ratio of HCl to HNO3 is 4:1.

Calculate moles of gold (Au)

Use the molar mass of gold (Au) to find the number of moles in 25.0 g: Molar mass of Au = 197.0 g/mol $$ \text{Moles of Au} = \frac{\text{mass}}{\text{molar mass}} = \frac{25.0 \text{ g}}{197.0 \text{ g/mol}} = 0.1269 \text{ mol} $$

Determine moles of Cl\(^-\) and NO\(_3^-\) ions needed

Use the stoichiometric ratio to calculate the moles of Cl\(^-\) and NO\(_3^-\) ions needed from HCl and HNO3, respectively: Moles of Cl\(^-\) (from HCl): \(0.1269 \text{ mol Au} \times \frac{4 \text{ mol Cl}^-}{1 \text{mol Au}} = 0.5076 \text{ mol Cl}^-\) Moles of NO\(_3^-\) (from HNO3): \(0.1269 \text{ mol Au} \times \frac{1 \text{ mol NO}_3^-}{1 \text{ mol Au}} = 0.1269 \text{ mol NO}_3^-\)

Calculate the volumes of HCl and HNO3 solutions

The moles of Cl\(^-\) and NO\(_3^-\) needed are known, so we can find the volumes of the HCl and HNO3 stock solutions required using their given molarities (12 M HCl solution and 16 M HNO3 solution): Volume of HCl solution: \(\frac{0.5076 \text{ mol Cl}^-}{12 \text{ M}}=0.0423 \text{ L}\) Volume of HNO3 solution: \(\frac{0.1269 \text{ mol NO}_3^-}{16 \text{ M}}=0.00794 \text{ L}\) (b) - Volume of 12 M HCl solution required: 0.0423 L - Volume of 16 M HNO3 solution: 0.00794 L

Key concepts

Stoichiometry

At its core, stoichiometry is the branch of chemistry that deals with the relative quantities of reactants and products in chemical reactions. It is rooted in the law of conservation of mass, where the total mass of the reactants equals the total mass of the products. In the context of dissolving gold using aqua regia, we need to understand the stoichiometry of the reaction to predict how much of each reactant is needed.

The stoichiometric ratio – the proportional relationship between the reactants based on the balanced chemical equation – is essential. For every mole of gold (Au), we need four moles of chloride ions (Cl^-) and one mole of nitrate ions (NO₃^-) to form the products. Therefore, stoichiometry allows us to deduce that the correct ratio of hydrochloric acid (HCl) to nitric acid (HNO₃) is 4:1, ensuring that each reactant contributes the correct number of ions needed for the reaction.

Chemical Reactions

Chemical reactions involve the transformation of one set of chemical substances into another. Each reaction is represented by a chemical equation that shows the reactants and the products with their respective chemical formulas. During the dissolution of gold with aqua regia, the balanced chemical equation helps us understand the molecular changes occurring.

In this reaction, solid gold reacts with chloride and nitrate ions, along with hydrogen ions, to produce chloroaurate ions, nitrogen monoxide, and water as products. Recognizing the reactants and products, as well as their physical states such as aqueous (aq), solid (s), or gas (g), is critical for comprehending how the reaction proceeds and how to control it.

Molarity Calculations

Molarity calculations are vital in chemistry, especially when preparing solutions or predicting the outcomes of reactions occurring in solution. The molarity (M) of a solution is defined as the number of moles of solute per liter of solution.

For our aqua regia example, knowing the molarity of HCl and HNO₃ solutions allows us to calculate the volumes needed to provide the requisite moles of Cl^- and NO₃^- ions for the reaction with gold. Using the formula volume = moles / molarity, we find the volume of each acid necessary to react with a given mass of gold. This conversion from mass to moles to volume is a critical application of molarity, enabling precise control over the quantities of reactants used, ultimately leading to successful chemical experimentation and industrial processes.