Question

In addition to the data found in Figure $9.13$, what other information do we need to find the mass of the sample of air used to determine the graph?

Short answer

The temperature of the gas has a value that is not present.

Step-by-step solution

Defining mass

The quantity of matter in a sample is known as its mass. Typically, mass is expressed in grams (g) and kilograms (kg).

Explanation

The ideal gas law equation is as follows:

$\mathrm{p}\mathrm{V}=\mathrm{n}\mathrm{R}\mathrm{T}$.

Here,$\mathrm{p}$ is the pressure, $\mathrm{V}$ is the volume, $\mathrm{n}$ is the number of molecules, $\mathrm{T}$ is the gas's temperature, and $\mathrm{R}$ is the gas constant. If we want to compute the mass of the air sample, we must first determine the value of $\mathrm{n}$.

$\mathrm{n}=\frac{\mathrm{p}\mathrm{V}}{\mathrm{R}\mathrm{T}}$.

Weneed to know the temperature value to compute the numberof molecules in the sample aswe get the values of$\mathrm{p}$ and $\mathrm{V}$from the graph, and $\mathrm{R}$ is a constant.

After we've determined the number of molecules, we can use the following formula to get the mass:

$\mathrm{m}=\mathrm{n}\times \mathrm{M}$

$\mathrm{M}$stands for molar mass. Air is a homogeneous mixture of many gases. The approximate molar mass of this combination, however, is $29$, which we may utilize in our computations.

Therefore, we may infer that the temperature of the gas sample is the sole parameter required to determine the mass of the gas sample.