Chapter U3, Problem SI5RE

(a)

Interpretation Introduction

Interpretation: Volume of $5.2\text{g}$ solid ${\text{CO}}_{\text{2}}$ needs to be explained.

Concept Introduction: According to Charles’ law, for a sample of gas, at constant temperature, the ratio of volume of gas to it’s Kelvin temperature is constant.

  $k\text{=}\frac{\text{V}}{\text{T}}$

The proportionality constant, k, is different for each different amount of gas.

Answer to Problem SI5RE

Volume of $5.2\text{g}$ of ${\text{CO}}_{\text{2}}$ is $3.33$ .

Explanation of Solution

The relationship between density, mass and volume is as follows:

  $\text{Density=}\frac{\text{Mass}}{\text{Volume}}$

If all the ${\text{CO}}_{\text{2}}$ is converted into gas from solid state, mass of converted ${\text{CO}}_{\text{2}}$ is same as the mass of the original solid ${\text{CO}}_{\text{2}}$ .

Given, mass of solid ${\text{CO}}_{\text{2}}$ is $5.2\text{g}$ and density of ${\text{CO}}_{\text{2}}$ is $1.56\text{g}$ .

Therefore,

  $\begin{array}{c}\text{Density=}\frac{\text{Mass}}{\text{Volume}}\\ \text{Volume}=\frac{\text{Mass}}{\text{Density}}\\ =\frac{5.2\text{}\text{g}}{1.56\text{g}}\\ =3.33\end{array}$

Therefore, volume of $5.2\text{g}$ of ${\text{CO}}_{\text{2}}$ is $3.33$ .

(b)

Interpretation Introduction

Interpretation: Volume of $5.2\text{g}$

  ${\text{CO}}_{\text{2}}$ needs to be explained.

Concept Introduction: According to Charles’ law, for a sample of gas, at constant temperature, the ratio of volume of gas to it’s Kelvin temperature is constant.

  $k\text{=}\frac{\text{V}}{\text{T}}$

The proportionality constant, k, is different for each different amount of gas.

Answer to Problem SI5RE

Volume of $5.2\text{g}$ of ${\text{CO}}_{\text{2}}$ is $2736.84\text{mL}$ .

Explanation of Solution

The relationship between density, mass and volume is as follows:

  $\text{Density=}\frac{\text{Mass}}{\text{Volume}}$

If all the ${\text{CO}}_{\text{2}}$ is converted into gas from solid state, mass of converted ${\text{CO}}_{\text{2}}$ is same as the mass of the original solid ${\text{CO}}_{\text{2}}$ .

Given, mass of solid ${\text{CO}}_{\text{2}}$ is $5.2\text{g}$ and density of ${\text{CO}}_{\text{2}}$ is $0.0019\text{g/mL}$ .

Therefore,

  $\begin{array}{c}\text{Density=}\frac{\text{Mass}}{\text{Volume}}\\ \text{Volume}=\frac{\text{Mass}}{\text{Density}}\\ =\frac{5.2\text{}\text{g}}{0.0019\text{g/mL}}\\ =2736.84\text{mL}\end{array}$

Therefore, volume of $5.2\text{g}$ of ${\text{CO}}_{\text{2}}$ is $2736.84\text{mL}$ .