Chapter 3, Problem 48E

What is the mass of each sample?

a.2.75 mol Fe

b.0.115 mol Al

c.125 mol Si

d.1 Ni atom

Interpretation Introduction

Interpretation:

The mass of each sample is to be calculated.

Concept Introduction:

 A mole is a unit of amount of substance. It relates the number of particles to the molar mass.

 One mole of a substance contains Avogadro’s number that is $6.022\times {10}^{23}$ particles. The number remains constant regardless of the nature of the substance. One mole of an atom contains $6.022\times {10}^{23}$ atoms. One mole of molecules contains $6.022\times {10}^{23}$ molecules.

 It also relates to the molar mass of a substance in grams. One mole of a substance weighs that amount in grams which is equal to its molar mass.

Answer to Problem 48E

a) $154\text{ g}$

b) $\text{3}\text{.10 g }$

c) $\text{35}\text{.1}\times {\text{10}}^3\text{ g }$

d) $9.746\times {10}^{-23}\text{ g}$

Explanation of Solution

a) $2.75$ mole Fe

The mass of Fe is calculated as follows:

The molar mass of Fe is $55.84\text{ g}$.

$\begin{array}{c}\text{Mass of 1 mole of Fe = 55}\text{.84 g}\\ \text{Mass of 2}\text{.75 mole of Fe = }\frac{\text{55}\text{.84 g}}{1\cancel{\text{mole}}}\times 2.75\cancel{\text{mole}}\\ \text{ = 154 g }\end{array}$

Therefore, the mass of Fe is $\text{154 g }$

b) $0.115$ moles Al

The mass of Al is calculated as follows:

The molar mass of Al is $27\text{ g}$.

$\begin{array}{c}\text{Mass of 1 mole of Al = 27 g}\\ \text{Mass of 0}\text{.115 moles of Al = }\frac{\text{27 g}}{1\cancel{\text{mole}}}\times 0.115\cancel{\text{mole}}\\ \text{ = 3}\text{.10 g }\end{array}$

Thus, the mass of Al is $3.10\text{ g}$.

c) $125$ moles Si

The mass of Si is calculated as follows:

The molar mass of Si is $28.1\text{ g}$.

$\begin{array}{c}\text{Mass of 1 mole of Si = 28}\text{.1 g}\\ \text{Mass of 125 moles of Si = }\frac{\text{28}\text{.1 g}}{1\cancel{\text{mole}}}\times 125\cancel{\text{mole}}\\ \text{ = 35}\text{.1}\times {\text{10}}^3\text{ g }\end{array}$

Hence, the mass of Si is $\text{35}\text{.1}\times {\text{10}}^3\text{ g }$.

d) $1$ Ni atom

The mass of Ni is calculated as follows:

The molar mass of Ni is $58.7\text{ g}$.

$\begin{array}{l}\text{6}\text{.022 }\times {\text{10}}^{23}\text{ atoms of Ni = 1 mole of Ni}\\ \text{1 atoms of Ni = }\frac{\text{ 1 mole}}{6.022\times {10}^{23}\cancel{\text{atoms}}}\times 1\cancel{\text{atoms}}\\ \text{ = 1}{\text{.67 × 10}}^{\text{-24}}\text{ moles}\\ \text{Mass of 1 mole of Ni = 58}\text{.7 g}\\ \text{Mass of 1}\text{.67 }\times {\text{10}}^{\text{-24}}\text{ moles of Ni = }\frac{1\cancel{\text{ atom Ni}}}{1}\times \frac{1\cancel{\text{mol Ni}}}{6.022\times {10}^{23}\cancel{\text{atom}}}\times \frac{\text{58}\text{.69 g}}{1\cancel{\text{mole}}}\\ \text{ = 9}\text{.746}\times {10}^{-23}\text{ g}\end{array}$

Hence, the mass of Ni is $\text{9}\text{.746}\times {10}^{-23}\text{ g}$.