Chapter 13, Problem 13.41P

Interpretation Introduction

Interpretation:

The molecular weight of each explosive in this chemical connection should be determined along with identify which explosive do the nitro groups contribute the largest percentage of molecular weight.

Concept Introduction:

The following explosives are present in the chemical connections.

Answer to Problem 13.41P

Molecular weight of TNT is $227.0$ amu and the percentage contribution of nitro group is $\text{60}\text{.79 \%}$

Molecular weight of nitroglycerine is.

$227.0$ amu and the percentage contribution of nitro group is $\text{60}\text{.79 \%}$

Molecular weight of cyclonite is.

$222.0$ amu and the percentage contribution of nitro group is.

$\text{62}\text{.16 \%}$

Molecular weight of pentaerythritol is $316.0$ amu and the percentage contribution of nitro group is $\text{58}\text{.22 \%}$

Therefore, cyclonite has high percentage contribution of nitro group in their molecular weight.

Explanation of Solution

Molecular weight of TNT (${\text{C}}_{\text{7}}{\text{H}}_{\text{5}}{\text{N}}_{\text{3}}{\text{O}}_{\text{6}}$):

Atomic weight of total number of carbon atoms = $\text{12}\text{.0 × 7 = 84}\text{.0}$

Atomic weight of total number of hydrogen atoms = $\text{1}\text{.0 × 5 = 5}\text{.0}$

Atomic weight of total number of nitrogen atoms = $\text{14}\text{.0 × 3 = 42}\text{.0}$

Atomic weight of total number of oxygen atoms = $\text{16}\text{.0 × 6 = 96}\text{.0}$

Molecular weight = $\text{84}\text{.0 + 5}\text{.0 + 42}\text{.0 + 96}\text{.0 = 227}\text{.0 amu}$

Therefore, molecular weight of TNT is $\text{227}\text{.0 amu}$

Percentage composition of ${\text{-NO}}_{\text{2}}$in TNT:

TNT has three ${\text{-NO}}_{\text{2}}$ groups.

Weight of.

${\text{-NO}}_{\text{2}}$ groups.

$\begin{array}{c}\text{= 3(14}\text{.0 + 2 × 16}\text{.0)}\\ \text{= 3 × 46}\text{.0}\\ \text{= 138}\text{.0 amu}\end{array}$

$\begin{array}{c}{\text{The contribution of NO}}_{\text{2}}\text{ = }\frac{\text{138}\text{.0}}{\text{227}\text{.0}}\text{×100\%}\\ \text{= 60}\text{.79\%}\end{array}$

Therefore, the percentage contribution of.

${\text{NO}}_{\text{2}}$ group is $\text{60}\text{.79\%}$

Percentage contribution of nitrogen in TNT:

TNT has three nitrogens.

$\begin{array}{c}\text{Weight of three nitrogens = 3(14}\text{.0)}\\ \text{= 42}\text{.0 amu}\end{array}$

$\begin{array}{c}\text{The contribution of Nitrogen = }\frac{\text{42}\text{.0}}{\text{227}\text{.0}}\text{×100 \%}\\ \text{= 18}\text{.50 \%}\end{array}$

Therefore, the percentage contribution of nitrogen in TNT is.

$\text{18}\text{.50 \%}$

Molecular weight of nitroglycerine (${\text{C}}_3{\text{H}}_{\text{5}}{\text{N}}_{\text{3}}{\text{O}}_9$):

Atomic weight of total number of carbon atoms = $\text{12}\text{.0 × 3 = 36}\text{.0}$

Atomic weight of total number of hydrogen atoms = $\text{1}\text{.0 × 5 = 5}\text{.0}$

Atomic weight of total number of nitrogen atoms = $\text{14}\text{.0 × 3 = 42}\text{.0}$

Atomic weight of total number of oxygen atoms = $\text{16}\text{.0 × 9 = 144}\text{.0}$

Molecular weight = $\text{36}\text{.0 + 5}\text{.0 + 42}\text{.0 + 144}\text{.0 = 227}\text{.0 amu}$

Therefore, molecular weight of nitroglycerine is $\text{227}\text{.0 amu}$

Percentage composition of ${\text{-NO}}_{\text{2}}$in nitroglycerine:

Nitroglycerine has three ${\text{-NO}}_{\text{2}}$ groups.

Weight of.

${\text{-NO}}_{\text{2}}$ groups.

$\begin{array}{c}\text{= 3(14}\text{.0 + 2 × 16}\text{.0)}\\ \text{= 3 × 46}\text{.0}\\ \text{= 138}\text{.0 amu}\end{array}$

$\begin{array}{c}{\text{The contribution of NO}}_{\text{2}}\text{ = }\frac{\text{138}\text{.0}}{\text{227}\text{.0}}\text{×100\%}\\ \text{= 60}\text{.79\%}\end{array}$

Therefore, the percentage contribution of.

${\text{NO}}_{\text{2}}$ group is $\text{60}\text{.79\%}$

Percentage contribution of nitrogen in nitroglycerine:

Nitroglycerine has three nitrogens.

$\begin{array}{c}\text{Weight of three nitrogens = 3(14}\text{.0)}\\ \text{= 42}\text{.0 amu}\end{array}$

$\begin{array}{c}\text{The contribution of Nitrogen = }\frac{\text{42}\text{.0}}{\text{227}\text{.0}}\text{×100 \%}\\ \text{= 18}\text{.50 \%}\end{array}$

Therefore, the percentage contribution of nitrogen in nitroglycerine is $\text{18}\text{.50 \%}$

Molecular weight of cyclonite (

${\text{C}}_3{\text{H}}_6{\text{N}}_6{\text{O}}_6$):

Atomic weight of total number of carbon atoms =.

$\text{12}\text{.0 × 3 = 36}\text{.0}$

Atomic weight of total number of hydrogen atoms =.

$\text{1}\text{.0 × 6 = 6}\text{.0}$

Atomic weight of total number of nitrogen atoms = $\text{14}\text{.0 × 6 = 84}\text{.0}$

Atomic weight of total number of oxygen atoms = $\text{16}\text{.0 × 6 = 96}\text{.0}$

Molecular weight = $\text{36}\text{.0 + 6}\text{.0 + 84}\text{.0 + 96}\text{.0 = 222}\text{.0 amu}$

Therefore, molecular weight of cyclonite is $\text{222}\text{.0 amu}$

Percentage composition of

${\text{-NO}}_{\text{2}}$in cyclonite:

Cyclonite has three ${\text{-NO}}_{\text{2}}$ groups.

Weight of ${\text{-NO}}_{\text{2}}$ groups.

$\begin{array}{c}\text{= 3(14}\text{.0 + 2 × 16}\text{.0)}\\ \text{= 3 × 46}\text{.0}\\ \text{= 138}\text{.0 amu}\end{array}$

$\begin{array}{c}{\text{The contribution of NO}}_{\text{2}}\text{ = }\frac{\text{138}\text{.0}}{\text{222}\text{.0}}\text{×100\%}\\ \text{= 62}\text{.16\%}\end{array}$

Therefore, the percentage contribution of.

${\text{NO}}_{\text{2}}$ group is.

$\text{62}\text{.16\%}$

Percentage contribution of nitrogen in cyclonite:

Cyclonite has six nitrogens.

$\begin{array}{c}\text{Weight of three nitrogens = 6(14}\text{.0)}\\ \text{= 84}\text{.0 amu}\end{array}$

$\begin{array}{c}\text{The contribution of Nitrogen = }\frac{\text{84}\text{.0}}{\text{222}\text{.0}}\text{×100 \%}\\ \text{= 37}\text{.84 \%}\end{array}$

Therefore, the percentage contribution of nitrogen in cyclonite is.

$\text{37}\text{.84 \%}$

Molecular weight of pentaerythritol (${\text{C}}_5{\text{H}}_8{\text{N}}_4{\text{O}}_{12}$):

Atomic weight of total number of carbon atoms = $\text{12}\text{.0 × 5 = 60}\text{.0}$

Atomic weight of total number of hydrogen atoms = $\text{1}\text{.0 × 8 = 8}\text{.0}$

Atomic weight of total number of nitrogen atoms = $\text{14}\text{.0 × 4 = 56}\text{.0}$

Atomic weight of total number of oxygen atoms =.

$\text{16}\text{.0 × 12 = 192}\text{.0}$

Molecular weight = $\text{60}\text{.0 + 8}\text{.0 + 56}\text{.0 + 192}\text{.0 = 316}\text{.0 amu}$

Therefore, molecular weight of pentaerythritol is $\text{316}\text{.0 amu}$

Percentage composition of ${\text{-NO}}_{\text{2}}$in pentaerythritol:

Pentaerythritol has four ${\text{-NO}}_{\text{2}}$ groups.

Weight of ${\text{-NO}}_{\text{2}}$ groups.

$\begin{array}{c}\text{= 4(14}\text{.0 + 2 × 16}\text{.0)}\\ \text{= 4 × 46}\text{.0}\\ \text{= 184}\text{.0 amu}\end{array}$

$\begin{array}{c}{\text{The contribution of NO}}_{\text{2}}\text{ = }\frac{\text{184}\text{.0}}{\text{316}\text{.0}}\text{×100\%}\\ \text{= 58}\text{.22\%}\end{array}$

Therefore, the percentage contribution of ${\text{NO}}_{\text{2}}$ group is $\text{58}\text{.22\%}$

Percentage contribution of nitrogen in pentaerythritol

Pentaerythritol has four nitrogens.

$\begin{array}{c}\text{Weight of four nitrogens = 4(14}\text{.0)}\\ \text{= 56}\text{.0 amu}\end{array}$

$\begin{array}{c}\text{The contribution of Nitrogen = }\frac{\text{56}\text{.0}}{\text{316}\text{.0}}\text{×100 \%}\\ \text{= 17}\text{.72 \%}\end{array}$

Therefore, the percentage contribution of nitrogen in pentaerythritol is $\text{17}\text{.72 \%}$.

Conclusion

Molecular weight of TNT is $227.0$ amu and the percentage contribution of nitro group is $\text{60}\text{.79 \%}$

Molecular weight of nitroglycerine is $227.0$ amu and the percentage contribution of nitro group is $\text{60}\text{.79 \%}$

Molecular weight of cyclonite is $222.0$ amu and the percentage contribution of nitro group is $\text{62}\text{.16 \%}$

Molecular weight of pentaerythritol is $316.0$ amu and the percentage contribution of nitro group is $\text{58}\text{.22 \%}$

Therefore, cyclonite has high percentage contribution of nitro group in their molecular weight.