Chapter 10.3, Problem 44PP

a.

Interpretation Introduction

Interpretation:

The number of carbon atoms in 52.0 g of carbon dioxide needs to be determined.

Concept introduction:

In 1 mol of any substance, there are $6.022\times {10}^{23}$ units of that substance. These units can be atoms and molecules. The number of units in 1 mol of any substance is known as Avogadro’s number. It is denoted by symbol N_A.

Answer to Problem 44PP

The number of carbon atoms present in one molecule of $C{O}_2$

$7.1\times {10}^{23}\text{ atoms}$.

Explanation of Solution

Given information:

A sample of carbon dioxide has a mass of $52g$.

Calculation:

The molar mass of carbon dioxide is 44 g/mol. Thus, from given mass, number of moles can be calculated as follows:

$\begin{array}{l}n=\frac{m}{M}\\ =\frac{52\text{ g}}{44\text{ g/mol}}\\ =1.18\text{ mol}\end{array}$

Now, from molecular formula, 1 mol of carbon dioxide has 1 mol of carbon thus, number of moles of carbon atom will be 1.18 mol.

The number of carbon atoms will be:

$\begin{array}{l}N=1.18\times N_A\\ =1.18\text{ mol}\times 6.022\times {10}^{23}\text{ atoms/mol}\\ =7.1\times {10}^{23}\text{ atoms}\end{array}$

b.

Interpretation Introduction

Interpretation:

The number of oxygen atoms in 52.0 g of carbon dioxide needs to be determined.

Concept introduction:

In 1 mol of any substance, there are $6.022\times {10}^{23}$ units of that substance. These units can be atoms and molecules. The number of units in 1 mol of any substance is known as Avogadro’s number. It is denoted by symbol N_A.

Answer to Problem 44PP

The number of oxygen atoms present in one molecule of $C{O}_2$ is $1.42\times {10}^{24}\text{atoms}$

Explanation of Solution

Given information:

A sample of carbon dioxide has a mass of $52g$.

Calculation:

The molar mass of carbon dioxide is 44 g/mol. Thus, from given mass, number of moles can be calculated as follows:

$\begin{array}{l}n=\frac{m}{M}\\ =\frac{52\text{ g}}{44\text{ g/mol}}\\ =1.18\text{ mol}\end{array}$

From the formula, 1 mol of carbon dioxide contains 2 mol of O atoms thus, the number of oxygen atoms in 1.18 mol of carbon dioxide will be:

$N=2\times 1.18\text{ mol}\left(6.022\times {10}^{23}\right)=1.42\times {10}^{24}\text{atoms}$

c.

Interpretation Introduction

Interpretation:

The mass in grams of 1 molecule of carbon dioxide needs to be determined.

Concept introduction:

In 1 mol of any substance, there are $6.022\times {10}^{23}$ units of that substance. These units can be atoms and molecules. The number of units in 1 mol of any substance is known as Avogadro’s number. It is denoted by symbol N_A.

Answer to Problem 44PP

The mass in grams in one molecule $C{O}_2$is $7.3\times {10}^{-23}\text{ g}$

Explanation of Solution

Given information:

A sample of carbon dioxide has a mass of $52g$.

Calculation:

The molar mass of carbon dioxide is 44 g/mol. Thus, from given mass, number of moles can be calculated as follows:

$\begin{array}{l}n=\frac{m}{M}\\ =\frac{52\text{ g}}{44\text{ g/mol}}\\ =1.18\text{ mol}\end{array}$

Now, mass of 1 mol of carbon dioxide is 44 g or mass of $6.022\times {10}^{23}$ molecules of carbon dioxide is 44 g.

Thus, the mass of 1 molecule will be:

$m=\frac{44\text{ g}}{6.022\times {10}^{23}\text{ molecule}}=7.3\times {10}^{-23}\text{ g}$