   Chapter 3, Problem 162CWP

Chapter
Section
Textbook Problem

Consider samples of phosphine (PH3), water (H2O), hydrogen sulfide (H2S), and hydrogen fluoride (HF), each with a mass of 119 g. Rank the compounds from the least to the greatest number of hydrogen atoms contained in the samples.

Interpretation Introduction

Interpretation: The given compounds are to be arranged from the least to the greatest number of hydrogen atoms contained in the samples.

Concept introduction: The number of moles in an atom is defined as the given mass divided by the molecular mass. One mole is equal to the Avogadro’s number and each element consists of different molar mass that depends on the weight of its atom. Number of atoms in an element is equal to the moles of that element multiplied by Avogadro’s number.

To determine: The rank of the given compounds from the least to the greatest number of hydrogen atoms contained in the samples.

Explanation

Explanation

Given

The samples are phosphine (PH3) , water (H2O) , hydrogen sulphide (H2S) and hydrogen fluoride (HF) .

The mass of each sample is 119 g .

The molar mass of (PH3) is 33.99 g/mol .

The molar mass of (H2O) is 18.0 g/mol .

The molar mass of (H2S) is 34.0 g/mol .

The molar mass of (HF) is 19.99 g/mol .

In phosphine (PH3) :

The number of moles is calculated by the formula,

Numberofmoles=GivenmassMolarmass

Substitute the value of the given mass and the molar mass, to calculate the number of moles of phosphine (PH3) , in the above equation.

NumberofmolesofPH3=GivenmassMolarmass=119 g33.99g/mol=3.50mol

The number of moles of (PH3) is 3.50 mol .

Number of hydrogen atoms is calculated by using the expression,

Number of H atoms=n×NA×Number of H in a given sample .

Where,

• n is the number of moles.
• NA=6.022×1023 is the Avogadro’s number.

Substitute the values of number of moles, NA and number of hydrogen in the above expression, the number of hydrogen atoms is calculated.

Number of H atoms=n×NA×Number of H in a given sample=3.50 mol×6.022×1023×3=6.3231×1024 atoms_

Hence, the number of hydrogen atoms in (PH3) is 6.3231×1024atoms_ .

In water (H2O) :

The number of moles is calculated by the formula,

Numberofmoles=GivenmassMolarmass

Substitute the value of the given mass and the molar mass, to calculate the number of moles of water (H2O) , in the above equation.

NumberofmolesofH2O=GivenmassMolarmass=119 g18.0g/mol=6.611mol

The number of moles of (H2O) is 6.611 mol .

Number of hydrogen atoms is calculated by using the expression,

Number of H atoms=n×NA×Number of H in a given sample .

Where,

• n is the number of moles.
• NA=6.022×1023 is the Avogadro’s number.

Substitute the values of number of moles, NA and number of hydrogen in the above expression, the number of hydrogen atoms is calculated.

Number of H atoms=n×NA×Number of H in a given sample=6.611 mol×6.022×1023×2=7.962×1024 atoms_

Hence, the number of hydrogen atoms in (H2O) is 7

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