Chapter 10, Problem 104A

(a)

Interpretation Introduction

Interpretation: The given data needs to be plotted if the density is plotted on the x-axis.

Concept Introduction: The molar mass and density of gases are directly proportional to each other.

Explanation of Solution

The given table for data showing the molar mass and density of seven gases at STP is as follows:

Substance	Molar mass (g/mol)	Density (g/L)
Oxygen	32	1.43
Carbon dioxide	44	1.96
Ethane	30	1.34
Hydrogen	2	0.089
Sulfur dioxide	64.1	2.86
Ammonia	17	0.759
Fluorine	38	1.70

Plotting graph by putting density at x -axis. Thus, the graph obtained will be:

  

(b)

Interpretation Introduction

Interpretation: The slope of the straight-line plot needs to be determined.

Concept Introduction: The slope of the straight line can be determined by simply finding the equation of a straight-line graph. To determine the value of the slope, display the equation on a graph.

Explanation of Solution

  

The equation for the graph is $y=22.416x-0.0219$ . It can be compared with the equation of a straight line as follows:

  $y=mx+c$

On comparing the slope of the graph is 22.416.

(c)

Interpretation Introduction

Interpretation: The molar mass of a gas at STP with a density of 1.10 g/L needs to be determined.

Concept Introduction: The slope of the straight line can be determined by simply finding the equation of a straight-line graph. To determine the value of the slope, display the equation on a graph.

Explanation of Solution

The graph equation is as follows:

  $y=22.416x-0.0219$

Since density is plotted on the x -axis put the value to calculate y which is the molar mass of gas corresponding to that volume.

  $\begin{array}{c}y=22.416\left(1.10\right)-0.0219\\ =24.64\end{array}$

Therefore, the molar mass of the gas is $24.64$ g/mol.

(d)

Interpretation Introduction

Interpretation The number of moles of a gas at STP needs to be calculated for mass 56.0 g.

Concept Introduction: The slope of the straight line can be determined by simply finding the equation of a straight-line graph. To determine the value of the slope, display the equation on a graph.

Explanation of Solution

According to the question, the number of moles of a gas is 1 mol at STP with a mass of 56.0 g. Thus, the molar mass is 56 g/mol.

The graph equation is as follows:

  $y=22.416x-0.0219$

Since density is plotted on the x -axis. Thus, the molar mass is at the y-axis.

  $\begin{array}{c}56\text{l }=22.416x-0.0219\\ 56\text{l+ }0.0219=22.416x\\ x=\frac{561.022}{22.416}\\ =25\end{array}$

Therefore, the molar mass of the gas is 25 g/L.