How many molecules of gas are contained in 5.6 dm3 of nitrogen at s.t.p.?

At s.t.p. (Standard Temperature and Pressure), 1 mole of any gas occupies $22.4 \text{ dm}^3$.

$$\text{Moles of N}_2 = \frac{\text{Volume of N}_2}{\text{Molar volume at s.t.p.}} = \frac{5.6 \text{ dm}^3}{22.4 \text{ dm}^3/\text{mol}} = 0.25 \text{ mol}$$

Avogadro's number states that 1 mole of any substance contains $6.022 \times 10^{23}$ particles (molecules in this case).

$$\text{Number of molecules} = \text{Moles of N}_2 \times \text{Avogadro's number}$$ $$\text{Number of molecules} = 0.25 \text{ mol} \times (6.022 \times 10^{23} \text{ molecules/mol})$$ $$\text{Number of molecules} = 1.5055 \times 10^{23} \text{ molecules}$$

The number of molecules of nitrogen gas is $1.5055 \times 10^{23} \text{ molecules}$.