Chapter 10, Problem 82E

Interpretation Introduction

Interpretation:

The gas among ${\text{H}}_{\text{2}}\text{S}$, ${\text{SO}}_{\text{3}}$, and ${\text{CF}}_{\text{2}}{\text{Cl}}_{\text{2}}$ that has a density of $5.40\text{g}/\text{L}$ at STP is to be identified.

Concept introduction:

The density is defined as the ratio of the mass of a body to its volume. The volume occupied by one mole of gas at different conditions of temperature and pressure is known as molar volume. The molar volume of all idea gas at STP is $22.4\text{L}/\text{mol}$.

Answer to Problem 82E

The gas among ${\text{H}}_{\text{2}}\text{S}$, ${\text{SO}}_{\text{3}}$, and ${\text{CF}}_{\text{2}}{\text{Cl}}_{\text{2}}$ that has a density of $5.40\text{g}/\text{L}$ at STP is ${\text{CF}}_{\text{2}}{\text{Cl}}_{\text{2}}$.

Explanation of Solution

The molar mass of the compound is the sum of the molar mass of individual elements present in it.

The molar mass of the hydrogen atom is $1.01\text{g}/\text{mol}$.

The molar mass of the sulfur atom is $32.07\text{g}{\text{mol}}^{-\text{1}}$.

$\begin{array}{rll}{\text{The molar mass of H}}_{\text{2}}\text{S}& =& 2\text{H}+\text{S}\\ & =& 2\times 1.01\text{g}/\text{mol}+32.07\text{g}/\text{mol}\\ & =& 2.02\text{g}/\text{mol}+32.07\text{g}/\text{mol}\\ & =& 34.09\text{g}/\text{mol}\end{array}$

The molar mass of the oxygen atom is $16.00\text{g}/\text{mol}$.

$\begin{array}{rll}\text{Molar}\text{mass}\text{of}{\text{SO}}_3\text{gas}& =& \text{S}+\left(3\times \text{O}\right)\\ & =& 32.07\text{g}/\text{mol}+\left(3\times 16.00\text{g}/\text{mol}\right)\\ & =& 32.07\text{g}/\text{mol}+48.00\text{g}/\text{mol}\\ & =& 80.07\text{g}/\text{mol}\end{array}$

The molar mass of the carbon atom is $12.01\text{g}/\text{mol}$.

The molar mass of the fluorine atom is $19.00\text{g}/\text{mol}$.

The molar mass of the chlorine atom is $35.45\text{g}/\text{mol}$.

$\begin{array}{rll}\text{Molar}\text{mass}\text{of}{\text{CF}}_{\text{2}}{\text{Cl}}_{\text{2}}\text{ gas}& =& \text{C}+\left(\text{2}\times \text{F}\right)+\left(2\times \text{Cl}\right)\\ & =& 12.01\text{g}/\text{mol}+\left(\text{2}\times 19.00\text{g}/\text{mol}\right)+\left(2\times 35.45\text{g}/\text{mol}\right)\\ & =& 12.01\text{g}/\text{mol}+38.00\text{g}/\text{mol}+70.9\text{g}/\text{mol}\\ & =& 120.91\text{g}/\text{mol}\end{array}$

The molar volume of all ideal gas at STP is $22.4\text{L}/\text{mol}$.

The density of a gas is given by the formula as shown below.

$D=\frac{M}{V}$ …(1)

Where,

• $V$ is the volume of the gas.

• $M$ is the mass of the gas.

Substitute the value of $V$ and molar mass of ${\text{H}}_{\text{2}}\text{S}$ in the equation (1).

$\begin{array}{rll}D& =& \frac{34.09\text{g}/\text{mol}}{22.4\text{L}/\text{mol}}\\ & =& 1.52\text{g}/\text{L}\end{array}$

Substitute the value of $V$ and molar mass of ${\text{SO}}_{\text{3}}$ in the equation (1).

$\begin{array}{rll}D& =& \frac{80.07\text{g}/\text{mol}}{22.4\text{L}/\text{mol}}\\ & =& 3.57\text{g}/\text{L}\end{array}$

Substitute the value of $V$ and molar mass of ${\text{CF}}_{\text{2}}{\text{Cl}}_{\text{2}}$ in the equation (1).

$\begin{array}{rll}D& =& \frac{120.91\text{g}/\text{mol}}{22.4\text{L}/\text{mol}}\\ & =& 5.40\text{g}/\text{L}\end{array}$

Therefore, ${\text{CF}}_{\text{2}}{\text{Cl}}_{\text{2}}$ has $5.40\text{g}/\text{L}$ density at STP.

Conclusion

The dichlorodifluoromethane $\left({\text{CF}}_{\text{2}}{\text{Cl}}_{\text{2}}\right)$ has $5.40\text{g}/\text{L}$ density at STP.