Question

Zinc and magnesium metal each react with hydrochloric acid according to the following equations: $$ \begin{array}{c} \mathrm{Zn}(s)+2 \mathrm{HCl}(a q) \longrightarrow \mathrm{ZnCl}_{2}(a q)+\mathrm{H}_{2}(g) \\ \mathrm{Mg}(s)+2 \mathrm{HCl}(a q) \longrightarrow \mathrm{MgCl}_{2}(a q)+\mathrm{H}_{2}(g) \end{array} $$ A \(10.00-\mathrm{g}\) mixture of zinc and magnesium is reacted with the stoichiometric amount of hydrochloric acid. The reaction mixture is then reacted with \(156 \mathrm{mL}\) of \(3.00 \mathrm{M}\) silver nitrate to produce the maximum possible amount of silver chloride. a. Determine the percent magnesium by mass in the original mixture. b. If \(78.0 \mathrm{mL}\) of HCl was added, what was the concentration of the HCl?

Short answer

The percent magnesium by mass in the original mixture is approximately 40.3%. The concentration of HCl added is approximately 6.00 M.

Step-by-step solution

Part A: Determine the percent magnesium by mass in the original mixture

Step 1: Calculate moles of silver nitrate We are given 156 mL of 3.00 M silver nitrate. To find the moles of silver nitrate, use the formula: moles = volume × concentration moles of silver nitrate = 0.156 L × 3.00 mol/L = 0.468 mol Step 2: Find moles of silver chloride formed The reaction between silver nitrate and the chlorides present in the produced solution from the first reaction is: AgNO3(aq) + ZnCl2(aq) + MgCl2(aq) → AgCl(s) + other products Since we are given the maximum possible amount of silver chloride produced, all silver nitrate reacts with the remaining chlorides: moles of silver chloride produced = moles of silver nitrate = 0.468 mol Step 3: Calculate moles of zinc and magnesium reacted From the balanced equation, we can derive the following stoichiometric relations for each reaction: - 1 mole of Zn reacts to form 1 mole of ZnCl2 - 1 mole of Mg reacts to form 1 mole of MgCl2 Let x moles of Zn and y moles of Mg react in the first reaction. Then, we derive the following equation based on the stoichiometry and the moles of silver chloride formed: 2x + 2y = 0.468 Step 4: Convert moles of Zn and Mg into mass Total mass of the mixture = 10.00 g From the molar mass of Zn (65.38 g/mol) and Mg (24.31 g/mol), we can write: 65.38x + 24.31y = 10.00 Step 5: Solve for x and y Now we have two equations with two unknowns (x and y): 1. 2x + 2y = 0.468 2. 65.38x + 24.31y = 10.00 Solving these two equations simultaneously, we get: x ≈ 0.0684 mol (Zn) y ≈ 0.1657 mol (Mg) Step 6: Calculate the percent magnesium by mass First, calculate the mass of magnesium in the mixture: mass of Mg = moles of Mg × molar mass of Mg mass of Mg = 0.1657 mol × 24.31 g/mol ≈ 4.03 g Now, calculate the percent magnesium by mass: percent Mg = (mass of Mg / total mass of mixture) × 100% percent Mg = (4.03 g / 10.00 g) × 100% ≈ 40.3% Therefore, the percent magnesium by mass in the original mixture is approximately 40.3%.

Part B: Find the concentration of HCl

Step 1: Calculate moles of HCl reacted Using the stoichiometry given in the balanced equations, we know the reaction ratio between both metals and HCl is 2:1. So, moles of HCl reacted = 2 × (moles of Zn + moles of Mg) moles of HCl reacted = 2 × (0.0684 + 0.1657) ≈ 0.468 mol Step 2: Calculate concentration of HCl We are given the volume of HCl added (78.0 mL). To find the concentration of HCl, use the formula: concentration = moles / volume concentration of HCl = 0.468 mol / 0.078 L ≈ 6.00 M Thus, the concentration of HCl added is approximately 6.00 M.

Key concepts

Moles Calculation

Understanding moles is fundamental in chemistry. A mole is a count, similar to a dozen, but instead of 12, a mole refers to Avogadro's number, which is approximately \(6.022 \times 10^{23}\). This allows chemists to count particles like atoms, molecules, or ions by weighing them. Calculating moles involves using the formula: \( \text{moles} = \text{mass} / \text{molar mass} \). For example, if you have 10 grams of a substance and its molar mass is 50 g/mol, you would have 0.2 moles of that substance.

• To find moles given a solution's volume and concentration, use: \( \text{moles} = \text{volume} \times \text{concentration} \).
• This is crucial in stoichiometry to find how much of each reactant is involved in a chemical reaction.

Chemical Reactions

Chemical reactions involve the transformation of substances through the breaking and forming of chemical bonds. Understanding the stoichiometry of reactions, which refers to using balanced chemical equations to determine the relative amounts of reactants and products, is key.For instance, in the reaction \(\text{Zn(s)} + 2 \text{HCl(aq)} \rightarrow \text{ZnCl}_2(\text{aq}) + \text{H}_2(\text{g})\), one mole of zinc reacts with two moles of hydrochloric acid to produce one mole of zinc chloride and one mole of hydrogen gas. This shows the mole ratio in which reactants combine and products form.

• Balancing chemical equations ensures that the same number of each type of atom appears on both sides of the equation, satisfying the law of conservation of mass.
• Stoichiometric coefficients indicate these proportions and are vital for calculating moles of substances involved in reactions.

Concentration

Concentration provides a measure of how much solute is present in a given volume of solution. The most common unit is molarity (M), which is moles of solute per liter of solution. In simpler terms, it tells us how "strong" or "weak" a solution is.To find concentration, the formula \( \text{concentration} = \text{moles} / \text{volume} \) is used. For example, if you dissolve 0.5 moles of a solute in 1 liter of water, the solution has a concentration of 0.5 M.

• Concentration influences how substances react, with higher concentrations generally leading to faster reactions due to more frequent particle interactions.
• Concentrations are crucial for determining the proportions required to reach equivalence in reactions, such as acid-base neutralization.

Percent Composition

Percent composition refers to the percentage by mass of each element in a compound. It helps identify the relative amounts of elements in a substance, and it's calculated using the formula: \[\text{percent composition} = \left( \frac{\text{mass of element in 1 mol of compound}}{\text{molar mass of compound}} \right) \times 100 \% \]In the context of mixtures, like in the given problem, finding the percent composition involves determining the fraction of the mixture contributed by each component.

• To calculate the percent composition of magnesium in a mixture: calculate the mass of magnesium, divide it by the total mass of the mixture, and multiply by 100%.
• This concept is essential in analyzing the makeup of compounds and ensuring the right mixture ratios in chemical processes.