Chapter 5, Problem 5.29PAE

5.29 What are the densities of the following gases at STP?

(a) CF₂Cl₂, (b)CO₂, (c) HCl

Interpretation Introduction

Interpretation:

The densities of the following gases at STP have to be calculated.

Concept Introduction:

• An ideal gas has is a hypothetical gas that is formed by a few molecules so that, its density is low, and the intermolecular forces are null. The model of gas facilitates mathematical calculations to study gases.
• The molar mass is mass expressed in grams of a mol of substance. The molar mass can be expressed is the following way,

$\text{M=}{\displaystyle \sum {\text{n}}_{\text{i}}{\text{A}}_{\text{i}}}$

Where n_i are the atoms number of element i that form the gas molecule gas and A_i is the atomic weight of element i.

• The ideal gas law can be expressed in the following way,

$\begin{array}{l}\text{P x V= n x R x T}\\ \text{P x V= }\frac{\text{m}}{\text{M}}\text{ x R x T}\\ \text{P = }\frac{\text{m}}{\text{V}}\text{ x }\frac{\text{R x T}}{\text{M}}\\ \text{P=δ x }\frac{\text{R x T}}{\text{M}}\end{array}$

Where P is the gas pressure (atm), V is the gas volume (L), T is the gas absolute temperature (K), n is the moles number of the gas , R is the ideal gas constant ( $\text{R=0}\text{.082 }\frac{\text{atm L}}{\text{K mol}}$ ), m is the mass (g) of the gas, ࢐ is the density of the gas and M (g/mol) is the molar mass of the gas.

In the STP conditions, the temperature is 273 K and the pressure is 1 atm.

Answer to Problem 5.29PAE

Solution: a) ${\text{δ}}_{{\text{CF}}_{\text{2}}{\text{Cl}}_{\text{2}}}=5.4\frac{\text{g}}{\text{L}}$

b) ${\text{δ}}_{{\text{CO}}_{\text{2}}}=1.96\frac{\text{g}}{\text{L}}$

c) ${\text{δ}}_{\text{HCl}}=1.63\frac{\text{g}}{\text{L}}$

Explanation of Solution

Given Information:

The following gases,$\begin{array}{l}{\text{a) CF}}_{\text{2}}{\text{Cl}}_{\text{2}}\\ {\text{b) CO}}_{\text{2}}\\ \text{c) HCl}\end{array}$

a)

1-Calculate the molar mass (M) of CF₂Cl₂,$\text{M= 1 x 12 }\frac{\text{g}}{\text{mol}}+\text{2 x 19}\frac{\text{g}}{\text{mol}}\text{ + 2 x 35}\text{.5 }\frac{\text{g}}{\text{mol}}=121\frac{\text{g}}{\text{mol}}$

2-Calculate the density of CF₂Cl₂ at STP$\begin{array}{l}{\text{1 atm = δ}}_{{\text{CF}}_{\text{2}}{\text{Cl}}_{\text{2}}}\text{x }\frac{\text{0}.082\frac{\text{atm L}}{\text{K mol}}\text{x 273 K}}{121\frac{\text{g}}{\text{mol}}}\\ \text{1 atm x }121\frac{\text{g}}{\text{mol}}={\text{δ}}_{{\text{CF}}_{\text{2}}{\text{Cl}}_{\text{2}}}\text{ x 0}.082\frac{\text{atm L}}{\text{K mol}}\text{x 273 K}\\ {\text{δ}}_{{\text{CF}}_{\text{2}}{\text{Cl}}_{\text{2}}}=\frac{\text{1 atm x ;}121\frac{\text{g}}{\text{m o l}}}{\text{0}.082\frac{\text{a t m L}}{\text{K ; m o l}}\text{x 273 K}}=5.4\frac{\text{g}}{\text{L}}\end{array}$

b)

1-Calculate the molar mass (M) of CO₂,$\text{M= 1 x 12 }\frac{\text{g}}{\text{mol}}+\text{2 x 16}\frac{\text{g}}{\text{mol}}\text{ = 44 }\frac{\text{g}}{\text{mol}}$

2-Calculate the density of CF₂Cl₂ at STP$\begin{array}{l}{\text{1 atm = δ}}_{{\text{CO}}_{\text{2}}}\text{x }\frac{\text{0}.082\frac{\text{atm L}}{\text{K mol}}\text{x 273 K}}{\text{44 }\frac{\text{g}}{\text{mol}}}\\ \text{1 atm x 44 }\frac{\text{g}}{\text{mol}}={\text{δ}}_{{\text{CO}}_{\text{2}}}\text{ x 0}.082\frac{\text{atm L}}{\text{K mol}}\text{x 273 K}\\ {\text{δ}}_{{\text{CO}}_{\text{2}}}=\frac{\text{1 atm x 44 }\frac{\text{g}}{\text{m o l}}}{\text{0}.082\frac{\text{a t m L}}{\text{K ; m o l}}\text{x 273 K}}=1.96\frac{\text{g}}{\text{L}}\end{array}$

c)

1-Calculate the molar mass (M) of HCl,$\text{M= 1 x 1 }\frac{\text{g}}{\text{mol}}+1\text{ x 35}\text{.5}\frac{\text{g}}{\text{mol}}\text{ = 36}\text{.5 }\frac{\text{g}}{\text{mol}}$

2-Calculate the density of CF₂Cl₂ at STP$\begin{array}{l}{\text{1 atm = δ}}_{\text{HCl}}\text{x }\frac{\text{0}.082\frac{\text{atm L}}{\text{K mol}}\text{x 273 K}}{\text{36}\text{.5 }\frac{\text{g}}{\text{mol}}}\\ \text{1 atm x 36}\text{.5 }\frac{\text{g}}{\text{mol}}={\text{δ}}_{\text{HCl}}\text{ x 0}.082\frac{\text{atm L}}{\text{K mol}}\text{x 273 K}\\ {\text{δ}}_{\text{HCl}}=\frac{\text{1 atm x 36}\text{.5 }\frac{\text{g}}{\text{m o l}}}{\text{0}.082\frac{\text{a t m L}}{\text{K ; m o l}}\text{x 273 K}}=1.63\frac{\text{g}}{\text{L}}\end{array}$

Conclusion

a) The density of CF₂Cl₂at STP is $5.4\frac{\text{g}}{\text{L}}$.

b) The density of CO₂at STP is $1.96\frac{\text{g}}{\text{L}}$.

c) The density of HCl at STP is $1.63\frac{\text{g}}{\text{L}}$.