Question 2

2. The equation $PV = Nk_BT$ describes the behaviour of an ideal gas.
   A student tests a fixed mass of gas to confirm that, for a constant temperature,
   $PV = K$
   where $K$ is a constant.
   The student does this by making measurements of $P$ and $V$.
   Five sets of data for this experiment are shown in the table. Four processed values of $\frac{1}{V}$ are also shown.

The variation of $P$ with $\frac{1}{V}$ is shown for four data points.

(a) (i) Plot the missing data point on the graph. [1]

(ii) Draw the best-fit line on the graph. [1]

(iii) Explain how the student can use the graph to decide whether the data support the relationship $PV = K$. [3]

(b) (i) Determine $K$. [2]

(ii) State an appropriate SI unit for $K$. [1]

(c) The laboratory is at a constant temperature of $291\,\text{K}$.
Determine the number of molecules in the fixed mass of gas. [1]