Chapter 8, Problem 28E

Interpretation Introduction

(a)

Interpretation:

The molar mass of ozone at STP density is to be calculated.

Concept introduction:

One mole of every gas occupies the same volume at STP. This value is equal to $\text{22}\text{.4}\text{L}$ and is known as the molar volume of the gas. The ratio of molar mass $\left(\text{g}\right)$ and the molar volume gives the value of density of the gas at STP. As the molar volume is the same for all the gases, the density depends only on the value of molar mass of the gas.

Answer to Problem 28E

The molar mass of ozone at STP density is $47.9\text{g}/\text{mol}$.

Explanation of Solution

The value of gas density for ozone is given as $\text{2}\text{.14}\text{g}/\text{L}$ and the value of molar volume is $\text{22}\text{.4}\text{L}/\text{mol}$.

The formula to calculate the gas density is given below.

$\text{Gas}\text{density}=\frac{\text{Molar}\text{mass}\text{in}\text{grams}}{\text{Molar}\text{volume}\text{in}\text{liters}}$

Rearrange the above equation to obtain the value of molar mass in grams.

$\begin{array}{rll}\text{Gas}\text{density}& =& \frac{\text{Molar}\text{mass}\text{in}\text{grams}}{\text{Molar}\text{volume}\text{in}\text{liters}}\\ \text{Molar}\text{mass}\text{in}\text{grams}& =& \text{Gas}\text{density}\times \text{Molar}\text{volume}\text{in}\text{liters}\end{array}$ …(1)

Substitute the values of gas density and molar volume in the above expression.

$\begin{array}{rll}\text{Molar}\text{mass}\text{in}\text{grams}& =& \text{Gas}\text{density}\times \text{Molar}\text{volume}\text{in}\text{liters}\\ & =& \text{2}\text{.14}\text{g}/\text{L}\times \text{22}\text{.4}\text{L}/\text{mol}\\ & =& 47.9\text{g}/\text{mol}\end{array}$

Therefore, the value of molar mass of ozone at STP density is $47.9\text{g}/\text{mol}$.

Conclusion

The molar mass of ozone at STP density is $47.9\text{g}/\text{mol}$.

Interpretation Introduction

(b)

Interpretation:

The molar mass of silane at STP density is to be calculated.

Concept introduction:

One mole of every gas occupies the same volume at STP. This value is equal to $\text{22}\text{.4}\text{L}$ and is known as the molar volume of the gas. The ratio of molar mass $\left(\text{g}\right)$ and the molar volume gives the value of density of the gas at STP. As the molar volume is the same for all the gases, the density depends only on the value of molar mass of the gas.

Answer to Problem 28E

The molar mass of silane at STP density is $32.0\text{g}/\text{mol}$.

Explanation of Solution

The value of gas density for silane is given as $\text{1}\text{.43}\text{g}/\text{L}$ and the value of molar volume is $\text{22}\text{.4}\text{L}/\text{mol}$.

The formula to calculate the gas density is given below.

$\text{Gas}\text{density}=\frac{\text{Molar}\text{mass}\text{in}\text{grams}}{\text{Molar}\text{volume}\text{in}\text{liters}}$

Rearrange the above equation to obtain the value of molar mass in grams.

$\begin{array}{rll}\text{Gas}\text{density}& =& \frac{\text{Molar}\text{mass}\text{in}\text{grams}}{\text{Molar}\text{volume}\text{in}\text{liters}}\\ \text{Molar}\text{mass}\text{in}\text{grams}& =& \text{Gas}\text{density}\times \text{Molar}\text{volume}\text{in}\text{liters}\end{array}$ …(1)

Substitute the values of gas density and molar volume in the above expression.

$\begin{array}{rll}\text{Molar}\text{mass}\text{in}\text{grams}& =& \text{Gas}\text{density}\times \text{Molar}\text{volume}\text{in}\text{liters}\\ & =& \text{1}\text{.43}\text{g}/\text{L}\times \text{22}\text{.4}\text{L}/\text{mol}\\ & =& 32.0\text{g}/\text{mol}\end{array}$

Therefore, the value of molar mass of silane at STP density is $32.0\text{g}/\text{mol}$.

Conclusion

The molar mass of silane at STP density is $32.0\text{g}/\text{mol}$.

Interpretation Introduction

(c)

Interpretation:

The molar mass of nitric oxide at STP density is to be calculated.

Concept introduction:

One mole of every gas occupies the same volume at STP. This value is equal to $\text{22}\text{.4}\text{L}$ and is known as the molar volume of the gas. The ratio of molar mass $\left(\text{g}\right)$ and the molar volume gives the value of density of the gas at STP. As the molar volume is the same for all the gases, the density depends only on the value of molar mass of the gas.

Answer to Problem 28E

The molar mass of nitric oxide at STP density is $30.0\text{g}/\text{mol}$.

Explanation of Solution

The value of gas density for nitric oxide is given as $\text{1}\text{.34}\text{g}/\text{L}$ and the value of molar volume is $\text{22}\text{.4}\text{L}/\text{mol}$.

The formula to calculate the gas density is given below.

$\text{Gas}\text{density}=\frac{\text{Molar}\text{mass}\text{in}\text{grams}}{\text{Molar}\text{volume}\text{in}\text{liters}}$

Rearrange the above equation to obtain the value of molar mass in grams.

$\begin{array}{rll}\text{Gas}\text{density}& =& \frac{\text{Molar}\text{mass}\text{in}\text{grams}}{\text{Molar}\text{volume}\text{in}\text{liters}}\\ \text{Molar}\text{mass}\text{in}\text{grams}& =& \text{Gas}\text{density}\times \text{Molar}\text{volume}\text{in}\text{liters}\end{array}$ …(1)

Substitute the values of gas density and molar volume in the above expression.

$\begin{array}{rll}\text{Molar}\text{mass}\text{in}\text{grams}& =& \text{Gas}\text{density}\times \text{Molar}\text{volume}\text{in}\text{liters}\\ & =& \text{1}\text{.34}\text{g}/\text{L}\times \text{22}\text{.4}\text{L}/\text{mol}\\ & =& 30.0\text{g}/\text{mol}\end{array}$

Therefore, the value of molar mass of nitric oxide at STP density is $30.0\text{g}/\text{mol}$.

Conclusion

The molar mass of nitric oxide at STP density is $30.0\text{g}/\text{mol}$.

Interpretation Introduction

(d)

Interpretation:

The molar mass of Freon-$22$ at STP density is to be calculated.

Concept introduction:

One mole of every gas occupies the same volume at STP. This value is equal to $\text{22}\text{.4}\text{L}$ and is known as the molar volume of the gas. The ratio of molar mass $\left(\text{g}\right)$ and the molar volume gives the value of density of the gas at STP. As the molar volume is the same for all the gases, the density depends only on the value of molar mass of the gas.

Answer to Problem 28E

The molar mass of Freon-$22$ at STP density is $86.5\text{g}/\text{mol}$.

Explanation of Solution

The value of gas density for Freon-$22$ is given as $\text{3}\text{.86}\text{g}/\text{L}$ and the value of molar volume is $\text{22}\text{.4}\text{L}/\text{mol}$.

The formula to calculate the gas density is given below.

$\text{Gas}\text{density}=\frac{\text{Molar}\text{mass}\text{in}\text{grams}}{\text{Molar}\text{volume}\text{in}\text{liters}}$

Rearrange the above equation to obtain the value of molar mass in grams.

$\begin{array}{rll}\text{Gas}\text{density}& =& \frac{\text{Molar}\text{mass}\text{in}\text{grams}}{\text{Molar}\text{volume}\text{in}\text{liters}}\\ \text{Molar}\text{mass}\text{in}\text{grams}& =& \text{Gas}\text{density}\times \text{Molar}\text{volume}\text{in}\text{liters}\end{array}$ …(1)

Substitute the values of gas density and molar volume in the above expression.

$\begin{array}{rll}\text{Molar}\text{mass}\text{in}\text{grams}& =& \text{Gas}\text{density}\times \text{Molar}\text{volume}\text{in}\text{liters}\\ & =& \text{3}\text{.86}\text{g}/\text{L}\times \text{22}\text{.4}\text{L}/\text{mol}\\ & =& 86.5\text{g}/\text{mol}\end{array}$

Therefore, the value of molar mass of Freon-$22$ at STP density is $86.5\text{g}/\text{mol}$.

Conclusion

The molar mass of Freon-$22$ at STP density is $86.5\text{g}/\text{mol}$.