Question

Zinc and magnesium metal each reacts with hydrochloric acid to make chloride salts of the respective metals, and hydrogen gas. A 10.00 -g mixture of zinc and magnesium produces 0.5171 g of hydrogen gas upon being mixed with an excess of hydrochloric acid. Determine the percent magnesium by mass in the original mixture.

Short answer

The percent magnesium by mass in the original mixture is 40.1%.

Step-by-step solution

Write the balanced chemical equations

Write the balanced chemical equations for both zinc and magnesium reacting with hydrochloric acid. For Zinc: Zn(s) + 2HCl(aq) → ZnCl₂(aq) + H₂(g) For Magnesium: Mg(s) + 2HCl(aq) → MgCl₂(aq) + H₂(g)

Calculate the moles of hydrogen gas produced

Using the mass of hydrogen gas produced, convert it into moles using its molar mass. Given mass of hydrogen gas = 0.5171 g Molar mass of H₂ = 2.016 g/mol Moles of hydrogen gas produced = mass of hydrogen gas / molar mass of H₂ = \( \frac{0.5171}{2.016} \) = 0.2568 mol

Express moles of zinc and magnesium in terms of hydrogen moles

Using stoichiometry and the balanced chemical equations, express the moles of zinc and magnesium in terms of moles of produced hydrogen gas. Let x mol of Zn react and y mol of Mg react. According to the balanced equation: Moles of Zn reacting = Moles of H₂ produced from zinc = x Moles of Mg reacting = Moles of H₂ produced from magnesium = y Total moles of hydrogen gas produced = Moles of H₂ produced from zinc + moles of H₂ produced from magnesium 0.2568 = x + y

Express the mass of zinc and magnesium in terms of moles

Express the mass of zinc and magnesium in terms of their moles and use the given total mass of the mixture to write an equation for the mass of zinc and magnesium. Mass of Zn = x * Molar mass of Zn = x * 65.38 g/mol Mass of Mg = y * Molar mass of Mg = y * 24.31 g/mol Total mass of mixture = Mass of Zn + Mass of Mg 10.00 g = 65.38x + 24.31y

Solve the system of equations

Solve the system of equations formed in Steps 3 and 4 to find the moles of zinc and magnesium. From Step 3: 0.2568 = x + y From Step 4: 10.00 = 65.38x + 24.31y Solve for x and y. We can use substitution or elimination to solve for x and y: By substitution, x = (0.2568 - y) Replace x in the second equation: 10.00 = 65.38(0.2568 - y) + 24.31y Solve for y: y = 0.1649 mol (moles of Mg) Now, substitute y back into the x equation: x = 0.2568 - 0.1649 = 0.0919 mol (moles of Zn)

Calculate the percent magnesium by mass

Now that we have the moles of magnesium, convert it to mass, and then calculate the percent magnesium by mass in the original mixture. Mass of Mg = 0.1649 * 24.31 g/mol = 4.010 g Percent magnesium by mass = \( \frac{Mass \, of \, Mg}{Total \, mass \, of \, mixture} \times 100 \) = \( \frac{4.010}{10.00} \times 100 \) = 40.1% The percent magnesium by mass in the original mixture is 40.1%.

Key concepts

Stoichiometry

Stoichiometry is at the heart of chemistry, allowing us to calculate the amount of reactants and products in a chemical reaction. In this problem, stoichiometry helps us determine the amount of hydrogen gas produced from a mixture of zinc and magnesium when reacting with hydrochloric acid. The key idea is to use the balanced chemical equations to find out how much of each metal produces the observed amount of hydrogen gas. By knowing the stoichiometric ratios, we can convert between moles and grams. This process informs us about how much of each element is consumed or produced in a reaction.

Chemical Reactions

Chemical reactions involve transformation of substances into new products. In the given problem, zinc and magnesium metals are reacting with hydrochloric acid. Each metal combines with acid to form metal chloride and hydrogen gas. The reaction for zinc is given by the formula \( \text{Zn(s)} + 2\text{HCl(aq)} \to \text{ZnCl}_2(\text{aq)} + \text{H}_2(\text{g)} \). Similarly, for magnesium, it is \( \text{Mg(s)} + 2\text{HCl(aq)} \to \text{MgCl}_2(\text{aq)} + \text{H}_2(\text{g)} \). These reactions illustrate how atoms are rearranged to form new compounds, confirming the conservation of mass.

Balanced Equations

Balanced chemical equations are crucial in stoichiometry as they show the precise ratio in which reactants turn into products. For every zinc atom that reacts, one molecule of hydrogen gas is produced, and the same is true for every magnesium atom. This is depicted in their balanced equations: \( \text{Zn(s)} + 2\text{HCl(aq)} \to \text{ZnCl}_2(\text{aq)} + \text{H}_2(\text{g)} \) and \( \text{Mg(s)} + 2\text{HCl(aq)} \to \text{MgCl}_2(\text{aq)} + \text{H}_2(\text{g)} \). The coefficients in these equations ensure that the number of atoms of each element is the same on both sides of the reaction, which is essential for any chemical calculation.

Percent Composition

Percent composition tells us how much of each component is present in a mixture compared to its total mass. In this exercise, we are focused on finding the percentage of magnesium in a zinc-magnesium mixture. We calculated the mass of magnesium produced from its moles and then determined its percent composition using the formula:

• Percent Magnesium = \( \frac{\text{Mass of Mg}}{\text{Total mass of mixture}} \times 100 \)

This calculation showed that magnesium constituted 40.1% of the original mixture by mass, illustrating its significance in the reaction and the effectiveness of stoichiometric calculations in determining the composition of reactants in a reaction.