   Chapter 15, Problem 20QAP ### Introductory Chemistry: A Foundati...

9th Edition
Steven S. Zumdahl + 1 other
ISBN: 9781337399425

#### Solutions

Chapter
Section ### Introductory Chemistry: A Foundati...

9th Edition
Steven S. Zumdahl + 1 other
ISBN: 9781337399425
Textbook Problem
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# Consider the iron alloy described in Question 19. Suppose it is desired to prepare 1.00 kg of this alloy, what mass of each component would be necessary?

Interpretation Introduction

Interpretation:

The mass of each component required to prepare 1.00kg of alloy is to be calculated.

Concept Introduction:

The mass percentage of a component present in a mixture is calculated by dividing the mass of the component present in the mixture by the total mass of the mixture and then multiplying it by 100. The formula for mass percentage is represented as:

mass%=MMt×100%

Where,

• M represents the mass of the component present in the mixture.
• Mt represents the total mass of mixture.
Explanation

The mass of carbon in the alloy is 2.59g.

The mass of chromium in the alloy is 1.59g.

The mass of iron in the alloy is 92.1g.

The formula for mass percentage is given as:

mass%=MMt×100%    (1)

Where,

• M represents the mass of the component present in the mixture.
• Mt represents the total mass of mixture.

Rearrange the above equation for the value of M.

M=mass%×Mt100%    (2)

The total mass of the steel is given as:

Mt=MC+MCr+MFe

Where,

• MC represents the mass of carbon in the steel.
• MNi represents the mass of nickel in the steel.
• MFe represents the mass of iron in the steel.

Substitute the value of mass of carbon, nickel and iron in the above equation.

Mt=2.59g+1.59g+92.1g=96.28g

The total mass of the alloy is 96.28g.

Substitute the value of mass of carbon and total mass of the alloy in the equation (1).

mass%=2.59g100%96.28g=2.69%

The mass percentage of carbon in the alloy is 2.69%.

Substitute the value of mass of nickel and total mass of the alloy in the equation (1).

mass%=1.59g100%96.28g=1

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