Chapter 10, Problem 1DE

(a)

Interpretation Introduction

To determine: The number of significant figures that are reported to determine the molar mass of gas.

Answer to Problem 1DE

Solution: The molar mass of the gas is reported up to 1 significant figure to identify the given noble gas.

Explanation of Solution

The given unknown gas is a noble gas and the difference in molar masses of noble gases is much larger. If the molar mass of unknown gas is reported correctly up to only one significant figure then it would be easily identified.

Conclusion

The molar mass of the gas is reported up to 1 significant figure to identify the given noble gas.

(b)

Interpretation Introduction

To determine: The experiment that could help in determining the molar mass of unknown gas and the tools, assumptions and the calculations used in the experiment.

Answer to Problem 1DE

Solution: The experiment that could help in determining the molar mass of unknown gas and the tools, assumptions and the calculations used in the experiment are as follows.

Explanation of Solution

The experiment that could help in determining the molar mass of unknown gas is as follow.
Mass of the empty mylar balloon is measured by the analytical balance. The balloon is then filled with unknown gas and is stored in a $\text{100}\text{mL}$ beaker, before this mass of empty $\text{100}\text{mL}$ beaker is measured. Add more and more filled balloons until the balloons reaches to the mark of $\text{100}\text{mL}$ . Then, weigh this balloon filled beaker using analytical balance and subtract the weight of empty balloons and the empty beaker.
The density of the gas is calculated as,

$d=\frac{m}{V}$

Where,

• $d$is the density of the gas.
• $m$ is the mass of the unknown gas.
• $V$ is the volume of the beaker.

It is assumed in the above equation that the volume occupied by the balloons is negligible.

The molar mass of the unknown gas is determined by the formula,

$d=\frac{P\times M}{R\times T}$

Where,

• $d$is the density of the gas.
• $P$ is the pressure of the gas.
• $R$ is the gas constant.
• $T$is the temperature at which experiment performed.
• $M$ is the molar mass of gas.

It is assumed that the gas is ideal in nature and with the help of above formula the molar mass of the unknown gas can be determined.

Conclusion

Conclusion:

The tools used in the experiment are analytical balance, mylar balloons and $\text{100}\text{mL}$ beaker.
The assumptions used in the experiment are volume of the balloons is taken as negligible and the gas is assumed to be ideal.
The formula used in the experiment for determining molar mass is,

$d=\frac{P\times M}{R\times T}$

(c)

Interpretation Introduction

To determine: The experimental method that is used to identify the given unknown gas.

Answer to Problem 1DE

Solution: The unknown gas can be identified on the basis of its molar mass.

Explanation of Solution

The unknown gas can be identified by determining its molar mass. The molar mass is determined by the instrument that has a gas jar filled with water that is connected to the bend tubes. As the gas is collected in the jar filled with water, the water level comes down. The volume is calculated by the volume of the gas jar and the mass is calculated by weighing the empty gas jar and filled gas jar.

The molar mass can be calculated by the formula,

$\frac{m}{V}=\frac{P\times M}{R\times T}$

Where,

• $m$is the mass of the gas.
• $V$ is the volume of the gas.
• $P$ is the pressure of the gas.
• $R$ is the gas constant.
• $T$is the temperature at which experiment performed.
• $M$ is the molar mass of gas.

The pressure of the gas is measured from the barometer.

Conclusion

The unknown gas can be identified by determining its molar mass with the help of the formula,
$\frac{m}{V}=\frac{P\times M}{R\times T}$