Chapter U3, Problem 5STP

Interpretation Introduction

Interpretation:

The volume of nitrogen gas produces when 50 mL of solid nitrogen sublimes needs to be calculated given the density of solid nitrogen is 1.026 g/cm³ and nitrogen gas is 0.00125 g/cm³.

Concept introduction:

The density of a substance is the mass occupied by it per unit volume i.e.

$\text{Density(D) = }\frac{\text{Mass (m)}}{\text{Volume (V)}}\text{ -----(1)}$

Answer to Problem 5STP

(B) 41 L

Explanation of Solution

Given:

Density of solid nitrogen = 1.026 g/cm³

Density of nitrogen gas = 0.00125 g/cm³

Volume of solid nitrogen = 50 mL

1 mL = 1 cm³

Calculation:

Calculate the mass of solid nitrogen as follows:

Based on equation (1):

$\begin{array}{l}\text{m = D}\times \text{V}\\ =1.026{\text{ g/cm}}^3\times 50{\text{ cm}}^3=51.3\text{ g}\end{array}$

Calculate the volume of nitrogen gas produced as follows:

Mass of solid nitrogen present = Mass of nitrogen produced = 51.3 g

$\begin{array}{l}{\text{Volume of N}}_2\text{ gas = }\frac{\text{m}}{\text{D}}\\ =\frac{51.3\text{ g}}{0.00125{\text{ g/cm}}^3}=41,040{\text{ cm}}^3\\ {\text{Since, 1000 cm}}^3\text{ = 1 liter}\\ \text{The corresponding volume = 41 L}\end{array}$

Conclusion

Thus, the volume of nitrogen gas produces when 50 mL of solid nitrogen sublimes is 41 L.