Chapter 3, Problem 13QAP

Complete the following table for TNT (trinitrotoluene), C₇H₅(NO₂)₃.

Interpretation Introduction

Interpretation:

The given table should be completed.

Concept introduction:

The number of moles of a substance is related to mass and molar mass as follows:

$n=\frac{m}{M}$

Here, m is mass and M is molar mass of the substance.

Also, according to Avogadro’s law in 1 mol of a substance there are $6.023\times {10}^{23}$ units of that substance. Here, $6.023\times {10}^{23}$ is known as Avogadro’s number and denoted by symbol $N_A$.

The density of a substance is related to mass and volume as follows:

$d=\frac{m}{V}$

Here, m is mass and V is volume.

Answer to Problem 13QAP

	Number of grams	Number of moles	Number of molecules	Number of N atoms
(a)	$127.2\text{ g}$	$0.56\text{ mol}$	$3.375\times {10}^{23}$	$9.0345\times {10}^{23}$
(b)	$210.1\text{ g}$	$0.9254\text{ mol}$	$5.57\times {10}^{23}$	$1.67\times {10}^{24}$
(c)	$4.67\times {10}^6\text{ g}$	$2.06\times {10}^4\text{ mol}$	$1.24\times {10}^{28}$	$3.72\times {10}^{28}$
(d)	$9.42\text{ g}$	$0.0415\text{ mol}$	$2.5\times {10}^{22}$	$7.5\times {10}^{22}$

Explanation of Solution

The given compound is TNT (trinitrotoluene) with molecular formula ${\text{C}}_{\text{7}}{\text{H}}_{\text{5}}{\left({\text{NO}}_{\text{2}}\right)}_{\text{3}}$. The molar mass of compound can be calculated as follows:

$M_{{\text{C}}_{\text{7}}{\text{H}}_{\text{5}}{\left({\text{NO}}_{\text{2}}\right)}_{\text{3}}}=7M_C+5M_H+3M_N+6M_O$

The molar mass of carbon, hydrogen, nitrogen and oxygen is 12 g/mol, 1 g/mol, 14 g/mol and 16 g/mol respectively.

Putting the values,

$\begin{array}{c}{M}_{{\text{C}}_{\text{7}}{\text{H}}_{\text{5}}{\left({\text{NO}}_{\text{2}}\right)}_{\text{3}}}=7\left(12\text{ g/mol}\right)+5\left(1\text{ g/mol}\right)+3\left(14\text{ g/mol}\right)+6\left(16\text{ g/mol}\right)\\ =\left(84+5+42+96\right)\text{g/mol}\\ =227\text{ g/mol}\end{array}$

Step (a)

The mass of TNT is 127.2 g. The number of moles can be calculated as follows:

$n=\frac{m}{M}$

Putting the values,

$\begin{array}{c}n=\frac{127.2\text{ g}}{227\text{ g/mol}}\\ =0.56\text{ mol}\end{array}$

Since, according to Avogadro’s law in 1 mol of a substance there are $6.023\times {10}^{23}$ units of that substance.

Thus, number of molecules in 0.56 mol of TNT will be:

$\begin{array}{c}N=0.56\text{ mol}\left(\frac{6.023\times {10}^{23}}{1\text{ mol}}\right)\\ =3.375\times {10}^{23}\end{array}$

Thus, number of molecules of TNT is $3.375\times {10}^{23}$.

Now, the molecular formula of TNT is ${\text{C}}_{\text{7}}{\text{H}}_{\text{5}}{\left({\text{NO}}_{\text{2}}\right)}_{\text{3}}$ thus, 1 mol TNT contains 3 mol of nitrogen. Thus, in 0.56 mol of TNT, number of moles of N will be:

$n=0.5\times 3=1.5\text{mol}$

Thus, number of N atoms will be:

$N_N=1.5\text{ mol}\left(\frac{6.023\times {10}^{23}}{1\text{ mol}}\right)=9.0345\times {10}^{23}$

Therefore, number of N atoms is $9.0345\times {10}^{23}$.

Step (b)

The number of moles of TNT is $0.9254\text{ mol}$ and molar mass of TNT is 227 g/mol thus, mass can be calculated as follows:

$m=n\times M$

Putting the values,

$\begin{array}{c}m=\left(0.9254\text{ mol}\right)\left(227\text{ g/mol}\right)\\ =210.1\text{ g}\end{array}$

The number of molecules of TNT can be calculated as follows:

$\begin{array}{c}N=\left(0.9254\text{ mol}\right)\left(\frac{6.023\times {10}^{23}}{1\text{ mol}}\right)\\ =5.57\times {10}^{23}\end{array}$

Now, in 1 mol there are 3 nitrogen atoms. Thus, the number of N atoms will be 3 times the number of molecules of TNT.

$\begin{array}{c}{N}_N=3\times 5.57\times {10}^{23}\\ =1.67\times {10}^{24}\end{array}$

Step (c)

The number of molecules of TNT is $1.24\times {10}^{28}$. Since, from the molecular formula 1 mol of TNT contains 3 N atoms.

Thus, number of N atoms in $1.24\times {10}^{28}$ molecules of TNT will be:

$\begin{array}{c}{N}_N=3\times 1.24\times {10}^{28}\\ =3.72\times {10}^{28}\end{array}$

According to Avogadro’s law, in mol there are $6.023\times {10}^{23}$ thus, number of moles from $1.24\times {10}^{28}$ number of molecules can be calculated as follows:

$\begin{array}{c}n=1.24\times {10}^{28}\left(\frac{1\text{ mol}}{6.023\times {10}^{23}}\right)\\ =2.06\times {10}^4\text{ mol}\end{array}$

Since, molar mass of TNT is 227 g/mol thus, mass can be calculated as follows:

$\begin{array}{c}m=n\times M\\ =\left(2.06\times {10}^4\text{ mol}\right)\left(227\text{ g/mol}\right)\\ =4.67\times {10}^6\text{ g}\end{array}$

Step (d)

The number of N atoms is $7.5\times {10}^{22}$.

Since, the number of N atoms is 3 times the number of TNT molecule. Thus, number of molecules of TNT will be:

$\begin{array}{c}N=\frac{7.5\times {10}^{22}}{3}\\ =2.5\times {10}^{22}\end{array}$

According to Avogadro’s law, in mol there are $6.023\times {10}^{23}$ thus, number of moles from $2.5\times {10}^{22}$ number of molecules can be calculated as follows:

$\begin{array}{c}n=2.5\times {10}^{22}\left(\frac{1\text{ mol}}{6.023\times {10}^{23}}\right)\\ =0.0415\text{ mol}\end{array}$

Since, molar mass of TNT is 227 g/mol thus, mass can be calculated as follows:

$\begin{array}{c}m=n\times M\\ =\left(0.0415\text{ mol}\right)\left(227\text{ g/mol}\right)\\ =9.42\text{ g}\end{array}$

Conclusion

Therefore, the complete table will be as follows:

	Number of grams	Number of moles	Number of molecules	Number of N atoms
(a)	$127.2\text{ g}$	$0.56\text{ mol}$	$3.375\times {10}^{23}$	$9.0345\times {10}^{23}$
(b)	$210.1\text{ g}$	$0.9254\text{ mol}$	$5.57\times {10}^{23}$	$1.67\times {10}^{24}$
(c)	$4.67\times {10}^6\text{ g}$	$2.06\times {10}^4\text{ mol}$	$1.24\times {10}^{28}$	$3.72\times {10}^{28}$
(d)	$9.42\text{ g}$	$0.0415\text{ mol}$	$2.5\times {10}^{22}$	$7.5\times {10}^{22}$