How many moles of molecules of each of the following gases would contain (a) 12dm³ of hydrogen at r.t.p?

At room temperature and pressure (r.t.p.), the molar volume of any gas is $24 \text{ dm}^3/\text{mol}$.

$$\text{Moles} = \frac{\text{Volume}}{\text{Molar Volume}}$$ $$\text{Moles of H}_2 = \frac{12 \text{ dm}^3}{24 \text{ dm}^3/\text{mol}} = 0.5 \text{ mol}$$

Avogadro's number ($N_A$) is $6.022 \times 10^{23} \text{ molecules/mol}$.

$$\text{Number of molecules} = \text{Moles} \times N_A$$ $$\text{Number of molecules of H}_2 = 0.5 \text{ mol} \times 6.022 \times 10^{23} \text{ molecules/mol}$$ $$= 3.011 \times 10^{23} \text{ molecules}$$

The number of moles of hydrogen gas is $\boxed{0.5 \text{ mol}}$ and the number of molecules is $\boxed{3.011 \times 10^{23} \text{ molecules}}$.