Ideal gas law, moles and Avogadro

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$PV = nRT = N k_B T$ — given in the data booklet. T must be in **kelvin**.

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A fixed-size 'pack' of particles: one mole = **6.02 × 10²³** particles (the **Avogadro constant** N_A).

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$N_A = 6.02 \times 10^{23}\ \text{mol}^{-1}$ — the number of particles in one mole. **Given**.

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$n = \dfrac{N}{N_A}$, so $N = n\,N_A$. **Given** in the data booklet.

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Use **R** (8.31) with the amount in **moles n**; use **k_B** (1.38 × 10⁻²³) with the **number of molecules N**. Never mix them.

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**Kelvin** (K). Convert from Celsius by adding 273.

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**Equal N** — same P, V, T means the same number of molecules, whatever the gas.

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Write $PV = NkT$ for each and **divide** one by the other — any equal quantity (P, V or T) cancels, leaving a simple ratio.

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$R = 8.31\ \text{J K}^{-1}\,\text{mol}^{-1}$ — used with the amount in moles. **Given**.

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$k_B = 1.38 \times 10^{-23}\ \text{J K}^{-1}$ — used with the number of molecules N. **Given**.

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$n = \dfrac{PV}{RT}$ — with P in Pa, V in m³, T in K.

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Leaving **T in Celsius** (must be kelvin), or mixing **n with k_B** / **N with R**.