An ideal gas at pressure $p = 2 \cdot 10^5$ Pa and temperature $T = 300$ K occupies a volume $V = 0.01$ m³. Find the amount of substance of the gas. The universal gas constant is $R = 8.31$ J/(mol·K).
The Mendeleev-Clapeyron equation: $pV = \nu RT$. Hence
$$\nu = \frac{pV}{RT} = \frac{2 \cdot 10^5 \cdot 0.01}{8.31 \cdot 300} = \frac{2000}{2493} \approx 0.80 \text{ mol}$$
$\nu \approx 0.80$ mol