A 15 litre cylinder holds oxygen at 290 K and 4.0 × 10⁵ Pa…

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A $15$ litre cylinder holds oxygen at $290\ \text{K}$ and $4.0 \times 10^{5}\ \text{Pa}$ . Find the number of moles, the number of molecules and the mass of the oxygen. (Molar mass $0.032\ \text{kg/mol}$ , $R = 8.31\ \text{J mol}^{-1}\text{K}^{-1}$ , $N_A = 6.02 \times 10^{23}\ \text{mol}^{-1}$ .)

Need a reminder? The key ideaShow

Ideal gas: $pV = nRT = Nk_BT$ , with $R = 8.31\ \text{J mol}^{-1}\text{K}^{-1}$ , $k_B = 1.38 \times 10^{-23}\ \text{J/K}$ , $N_A = 6.02 \times 10^{23}\ \text{mol}^{-1}$ . For a fixed amount, $\dfrac{p_1V_1}{T_1} = \dfrac{p_2V_2}{T_2}$ . Always use kelvin. A constant-volume gas thermometer reads $T = 273.16\ \text{K} \times \dfrac{p}{p_{\text{tp}}}$ .

The worked solution

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