   # A mixture of chromium and zinc weighing 0.362 g was reacted with an excess of hydrochloric acid. After all the metals in the mixture reacted, 225 mL dry of hydrogen gas was collected at 27°C and 750. torr. Determine the mass percent of Zn in the metal sample. [Zinc reacts with hydrochloric acid to produce zinc chloride and hydrogen gas; chromium reacts with hydrochloric acid to produce chromium(III) chloride and hydrogen gas.] ### 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 8, Problem 152CP
Textbook Problem
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## A mixture of chromium and zinc weighing 0.362 g was reacted with an excess of hydrochloric acid. After all the metals in the mixture reacted, 225 mL dry of hydrogen gas was collected at 27°C and 750. torr. Determine the mass percent of Zn in the metal sample. [Zinc reacts with hydrochloric acid to produce zinc chloride and hydrogen gas; chromium reacts with hydrochloric acid to produce chromium(III) chloride and hydrogen gas.]

Interpretation Introduction

Interpretation: The mass percent of Zn in the given mixture of 0.362g sample containing chromium and zinc which react with HCl and producing 225mL of H2 at 27oC and 750torr is needed to be determined if the other products are zinc chloride and chromium (III) chloride.

Concept introduction:

• Number of moles of a substance, According to ideal gas equation,

Numberofmoles=Pressure×VolumeR×Temperature

• Mole ratios between the reactant and a product of a reaction are depends upon the coefficients of reactant and product in a balanced chemical equation.
• Mass of a substance from its number of moles is,

Number of moles×Molecularmass in grams=takenmass

• Mass percentages of substances in a mixture of sample are the ratio of mass of substance reacted to mass of whole sample taken.

To determine: the mass percent of Zn in the given mixture of 0.362g sample containing chromium and zinc.

### Explanation of Solution

To find: the number of moles of producing 225mL of H2 at 27oC and 750torr in the given reaction.

The number of moles of produced H2 is 9.02×103mol .

The pressure of produced H2 is given as 750torr=750torr×1atm760torr=0.9868atm .

The volume of produced H2 is given as 225mL=0.225L .

The temperature is given as 27oC=(27+273)K=300K .

The equation for finding number of moles of a substance, According to ideal gas equation,

Numberofmoles=Pressure×VolumeR×Temperature

Therefore,

The number of moles of produced H2 is,

Numberofmoles=0.9868atm×0.225L0.08206Latm/Kmol×300K =9.02×103mol

Hence, the number of moles of produced H2 is 9.02×103mol .

To find: the balanced equations for given reactions.

Cr+3HClCrCl3+32H2

Zn+2HClZnCl2+H2

The reactants presented are Cr,ZnandHCl .

The products of the given reactions are CrCl3,H2andZnCl2 .

Therefore,

The chemical equations for the given reactions are,

Cr+HClCrCl3+H2

Zn+HClZnCl2+H2

This equations are not balanced, Balanced equation is the chemical equation of a reaction which is written according to law of conservation of mass the mass of reactant molecules should conserve in product molecules.

The balanced chemical equations of the given reactions are,

Balance the molecules in both sides of arrow in order of atoms other than hydrogen then hydrogen atoms.

Therefore, the above equation of given reaction will become,

Cr+3HClCrCl3+32H2

Zn+2HClZnCl2+H2

Hence, the balanced equation for given reaction is,

Cr+3HClCrCl3+32H2

Zn+2HClZnCl2+H2

To find: the masses of chromium and zinc reacted in the given reaction

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