Chapter 3, Problem 177CP

### Chemistry

10th Edition
Steven S. Zumdahl + 2 others
ISBN: 9781305957404

Chapter
Section

### Chemistry

10th Edition
Steven S. Zumdahl + 2 others
ISBN: 9781305957404
Textbook Problem

# 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

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 65.38Â g/mol..

The molar mass of H2 is,

2Ã—1.008â€‰g/molÂ =Â 2.016Â g/molâ€‰

The mass of magnesium is assumed to be xâ€‰g.

Since, the gaseous mixture consists of only magnesium and zinc, therefore, mass of zinc is 10gÂ -Â xÂ gÂ .

Formula

The number of moles is calculated by using the formula,

Numberâ€‰ofâ€‰molesâ€‰â€‰=â€‰Givenâ€‰massMolarâ€‰mass (1)

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

NumberÂ ofÂ molesÂ ofâ€‰Mgâ€‰=â€‰xâ€‰g24.31â€‰g/mol

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

NumberÂ ofÂ molesÂ ofâ€‰Znâ€‰=â€‰10gÂ -Â xâ€‰g65.38â€‰g/mol

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

NumberÂ ofÂ molesÂ ofâ€‰H2â€‰=â€‰0.5176g2.016Â g/mol

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

Znâ€‰+â€‰2HClâ€‰â€‰â€‰â€‰â†’â€‰â€‰â€‰ZnCl2+H2Mgâ€‰+â€‰2HClâ€‰â€‰â†’â€‰â€‰â€‰MgCl2+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,

NumberÂ ofÂ molesÂ ofÂ hydrogenÂ =(MolesÂ ofÂ ZincÂ +Â MolesÂ ofÂ Magnesium)

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

NumberÂ ofÂ molesÂ ofÂ hydrogenÂ =(MolesÂ ofÂ ZincÂ +Â MolesÂ ofÂ Magnesium)â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰â€‰[0

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started