   # 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. ### Chemistry: An Atoms First Approach

2nd Edition
Steven S. Zumdahl + 1 other
Publisher: Cengage Learning
ISBN: 9781305079243

#### Solutions

Chapter
Section ### Chemistry: An Atoms First Approach

2nd Edition
Steven S. Zumdahl + 1 other
Publisher: Cengage Learning
ISBN: 9781305079243
Chapter 5, Problem 167CP
Textbook Problem
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## 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.

Interpretation Introduction

Interpretation: The mass of gaseous mixture that contains zinc and magnesium is given. Also mass of hydrogen produced during this reaction is given. By using these values, the mass percent of magnesium in the mixture is to be calculated.

Concept introduction: The molar mass of any compound can be calculated by adding of atomic weight of individual atoms present in it.

The number of moles is the ratio of mass of compound to its molar mass.

To determine: The mass percent of magnesium.

### Explanation of Solution

Given

The mass of mixture is 10.00g..

The mass of hydrogen produced is 0.5171g.

The atomic mass of magnesium is 24.31g/mol..

The atomic mass of zinc is 65.38 g/mol..

The molar mass of H2 is,

2×1.008g/mol = 2.016 g/mol

The mass of magnesium is assumed to be xg.

Since, the gaseous mixture consists of only magnesium and zinc, therefore, mass of zinc is 10g - x g .

Formula

The number of moles is calculated by using the formula,

Numberofmoles=GivenmassMolarmass (1)

Substitute the values of mass and molar mass of magnesium in above equation.

Number of moles ofMg=xg24.31g/mol

Substitute the values of mass and molar mass of zinc in above equation.

Number of moles ofZn=10g - xg65.38g/mol

Substitute the values of mass and molar mass of hydrogen gas in equation (1).

Number of moles ofH2=0.5176g2.016 g/mol

The reaction of magnesium and zinc with hydrochloric acid HCl is,

Zn+2HClZnCl2+H2Mg+2HClMgCl2+H2

Since, two moles of hydrogen is produced by two moles of either zinc or magnesium.

Hence,

The number of moles of hydrogen in the reaction is calculated by,

Number of moles of hydrogen =(Moles of Zinc + Moles of Magnesium)

Substitute the values of moles of hydrogen, zinc and magnesium in above equation,

Number of moles of hydrogen =(Moles of Zinc + Moles of Magnesium)[0

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