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Chapter 3: Problem 177

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

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

Step by step solution

01

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)
02

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
03

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
04

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
05

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)
06

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%.

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