   # A sample of a hydrocarbon (a compound consisting of only carbon and hydrogen) contains 2.59 × 10 23 atoms of hydrogen and is 17.3% hydrogen by mass. If the molar mass of the hydrocarbon is between 55 and 65 g/mol, what amount (moles) of compound is present, and what is the mass of the sample? ### 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 139AE
Textbook Problem
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## A sample of a hydrocarbon (a compound consisting of only carbon and hydrogen) contains 2.59 × 1023 atoms of hydrogen and is 17.3% hydrogen by mass. If the molar mass of the hydrocarbon is between 55 and 65 g/mol, what amount (moles) of compound is present, and what is the mass of the sample?

Interpretation Introduction

Interpretation: A sample of a hydrocarbon is given. The amount (moles) of the compound present and the mass of the sample is to be calculated.

Concept introduction: The number of moles of a substance is calculated by the formula,

Numberofmoles=GivenmassofthesubstanceMolarmassofthesubstance

To determine: The amount (moles) of the compound present and the mass of the given sample.

### Explanation of Solution

To determine: The mass of the given sample.

Given

The given hydrocarbon contains 2.59×1023atoms of hydrogen.

Molar mass of the hydrocarbon lies between 55g/mol and 65g/mol .

The sample contains 17.3% of hydrogen by mass.

The number of moles of hydrogen having 6.022×1023atoms =1mol

The number of moles of hydrogen having 1atom =(16.022×1023)mol

The number of moles of hydrogen having 2.59×1023atoms =(1×2.59×10236.022×1023)mol=0.4300mol

The mass of 1mol of hydrogen =1g

The mass of 0.4300mol of hydrogen =0.4300g

The total mass of the sample is assumed to be x ”.

The sample contains 17.3% of hydrogen by mass.

Therefore, 17.3%ofx=0.4300g

Simplify the above expression.

x=(0.4300×10017.3)g=2.5g_

To determine: The amount (moles) of the compound present.

The sample contains 17.3% of hydrogen by mass.

The mass percent of carbon in the sample =(10017.3)%=82.7%

The mass of carbon in the sample is calculated by the formula,

Massofcarbon=Masspecentofcarbon×Massofcompound

Substitute the value of mass percent of carbon and the mass of the compound in the above expression.

Massofcarbon=(82.7100×2.5)g=2.07g

Formula

The number of moles of a substance is calculated by the formula,

Numberofmoles=GivenmassofthesubstanceMolarmassofthesubstance

Substitute the value of the given mass and the molar mass of carbon in the above expression

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