R = 8.31
Formula
The ideal gas equation of state links pressure, volume, amount of substance and temperature: pV = νRT.
ENT-level problem
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
$$\nu = \frac{pV}{RT} = \frac{2 \cdot 10^5 \cdot 0.01}{8.31 \cdot 300} = \frac{2000}{2493} \approx 0.80 \text{ mol}$$
The Mendeleev–Clapeyron equation written in moles states that for a gas of fixed mass the ratio pV to temperature does not change. The gas constant is R = 8.31 J/(mol·K), and ν = m / M is the amount of substance in moles.
The temperature must be in kelvins (T = t + 273), pressure in pascals and volume in cubic metres. Isothermal processes and the work of the gas are calculated from this equation.
Divide the mass of the gas by its molar mass: ν = m / M. For example, 4.4 g of CO₂ is 0.1 mol.
p in pascals, V in m³, ν in moles, T in kelvins — then R = 8.31 J/(mol·K).
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