Chapter 21, Problem 17STP

Interpretation Introduction

Interpretation:

The mass of nitrogen in grams should be determined when total mass of compound is 475 g.

1. 33.93 g
2. 52.78 g
3. 67.86 g
4. 109.0 g
5. 110.5 g

Concept introduction:

Number of moles is equal to the ratio of given mass to the molar mass.

The mathematical expression is given by:

Number of moles = $\frac{\text{mass}}{\text{Molar mass}}$

Molar mass of the molecule is equal to the sum of the masses of atoms present in the molecule.

Answer to Problem 17STP

Mass of nitrogen in 475 g of compound is $109.00\text{ g}$. Thus, option (D) is correct.

Explanation of Solution

According to the given figure,

Percentage of carbon = 19.68 %

Percentage of oxygen = 52.42 %

Percentage of hydrogen = 4.96 %

Percentage of nitrogen = 22.95 %

Let, total mass of the compound = 100 grams.

Thus, mass of carbon ( $\text{C}$ ) = 19.68 g

Mass of oxygen ( $\text{O}$ ) = 52.42 g

Mass of hydrogen ( $\text{H}$ ) = 4.96 g

Mass of nitrogen ( $\text{N}$ ) = 22.95 g

Now,

Molar mass of carbon = 12.011 g/mole

Number of moles of carbon = $\frac{19.68\text{ g}}{\text{12}\text{.011 g/mole}}$

= $\text{1}\text{.64 mole}$

Molar mass of oxygen = 15.999 g/mole

Number of moles of oxygen = $\frac{52.42\text{ g}}{\text{15}\text{.999 g/mole}}$

= $\text{3}\text{.28 mole}$

Molar mass of hydrogen = 1.008 g/mole

Number of moles of hydrogen = $\frac{4.96\text{ g}}{\text{1}\text{.008 g/mole}}$

= $\text{4}\text{.92 mole}$

Molar mass of nitrogen = 14.007 g/mole

Number of moles of nitrogen = $\frac{\text{22}\text{.95 g}}{\text{14}\text{.007 g/mole}}$

= $\text{1}\text{.64 mole}$

Divide each number of moles by smallest number 1.64.

Number of moles of carbon = $\frac{\text{1}\text{.64 mole}}{\text{1}\text{.64 mole}}$

= 1 mole

Number of moles of oxygen = $\frac{\text{3}\text{.28 mole}}{\text{1}\text{.64 mole}}$

= 2 moles

Number of moles of hydrogen = $\frac{\text{4}\text{.92 mole}}{\text{1}\text{.64 mole}}$

= 3 moles

Number of moles of nitrogen = $\frac{\text{1}\text{.64 mole}}{\text{1}\text{.64 mole}}$

= 1 mole

Thus, the formula of compound is ${\text{CH}}_{\text{3}}{\text{NO}}_{\text{2}}$.

Total mass of compound is 475 g.

Molar mass of ${\text{CH}}_{\text{3}}{\text{NO}}_{\text{2}}$ = 61.04 g/mole.

Number of moles of ${\text{CH}}_{\text{3}}{\text{NO}}_{\text{2}}$ = $\frac{\text{475 g}}{\text{61}\text{.04 g/mole}}$

$\text{= 7}\text{.78 mole}$

In ${\text{CH}}_{\text{3}}{\text{NO}}_{\text{2}}$, one mole of nitrogen is present.

Number of moles of nitrogen = 1 mole

Molar mass of nitrogen = 14.007 g/mole

Thus, mass of nitrogen in 475 g of compound = $\text{7}\text{.78 mole}\times \text{ 14}\text{.007 g/mole}$

= $108.97\text{ g}$

Mass of nitrogen = $109.00\text{ g}$

Hence, option (D) is correct.