IB DP Physics Mock Exam HL Paper 1B Set 4 - 2025 Syllabus

(a)
(i) Calculate \(\frac{1}{V}\) for the missing value: \(\frac{1}{1.54 \times 10^{-5}} \approx 6.49 \times 10^{4}\,m^{-3}\).
Plot the point at \((6.5 \times 10^{4}, 10.3 \times 10^{4})\) on the graph.
(ii) Draw a single straight best-fit line so that the data points are evenly distributed about it.
(iii) If \(PV = K\), then \(P = K \times \frac{1}{V}\), so the graph should be a straight line passing through the origin.

(b)
(i) The value of \(K\) is equal to the gradient of the best-fit line:
\[K = \frac{\Delta P}{\Delta (1/V)} \approx 1.56\]
(ii) Suitable SI units include joules (\(J\)), newton metres (\(Nm\)), or pascal cubic metres (\(Pa\,m^{3}\)).

(c)
Using \(PV = Nk_{B}T\) and \(PV = K\):
\[N = \frac{K}{k_{B}T}\]
Substituting \(K \approx 1.56\), \(T = 291\,K\), and \(k_{B} = 1.38 \times 10^{-23}\,J\,K^{-1}\):
\[N \approx 3.96 \times 10^{20}\]
The number of molecules is approximately \(4.0 \times 10^{20}\).