Question

To determine the mass of neon contained in a rigid, $2.0L$cylinder, you vary the cylinder’s temperature while recording the reading of a pressure gauge. Your data are as follows:

Temperature (°C)	Pressure gauge (atm)
100	6.52
150	7.80
200	8.83
250	9.59

Use the best-fit line of an appropriate graph to determine the mass of the neon.

Short answer

Using the best-fit line of the appropriate graph, the determined mass of the neon is$\mathbf{9}\mathbf{.}\mathbf{62}\mathbf{}\mathit{g}$

Step-by-step solution

Defining ideal gas law and molar mass

The law of ideal gas and the number of moles $n$is given by $n=\frac{m}{M}$, where $m$is the mass of the substance and $M$is its molar mass.

So we can write the following
$$\begin{gathered} PV=nRT \\ \Rightarrow T=\frac{pV}{nR} \end{gathered}$$
By substituting $n$we get
$T=\frac{VM}{mR}p$

Making the graph of temperature as a function of pressure 

With the given data points, we can make a graph of temperature as a function of pressure.

After converting the pressure to Pa and the temperature to K, we get something like the following result:

Calculating the mass of the neon. 

The equation for $T$is a linear relationship whose slope we know from fitting (which can even be done in Excel with the "trend line" command). If we specify the slope with$a$, we can write
$$\begin{gathered} a=\frac{VM}{m.R} \\ \Rightarrow m=\frac{VM}{a.R} \\ =\frac{0.002\times 20}{0.0005\times 8.31} \\ =\mathbf{9}\mathbf{.}\mathbf{62}\mathbf{}\mathit{g} \end{gathered}$$