Given data

• Molarity of solution: $M = 2 \times 10^{-1} = 0.2\,\text{mol L}^{-1}$
• Volume of solution: $500\,\text{mL} = 0.5\,\text{L}$
• Density of solution: $1.25\,\text{g mL}^{-1}$
• Solute: anhydrous $\text{CuSO}_4$

Find moles of $\text{CuSO}_4$ in 500 mL solution

Using $\text{moles} = M \times V$ $n = 0.2 \times 0.5 = 0.1\,\text{mol}$

Find mass of solute

Molar mass of $\text{CuSO}_4$: $M_r = 63.5 + 32 + 4(16) = 159.5\,\text{g mol}^{-1}$

So mass of solute is $m_{\text{solute}} = 0.1 \times 159.5 = 15.95\,\text{g}$

Find mass of solution

Using density, $\text{mass of solution} = 1.25 \times 500 = 625\,\text{g}$

Find mass of solvent (water)

$m_{\text{solvent}} = 625 - 15.95 = 609.05\,\text{g} = 0.60905\,\text{kg}$

Calculate molality

$\text{molality} = \frac{\text{moles of solute}}{\text{kg of solvent}}$ $m = \frac{0.1}{0.60905} = 0.16419\,\text{mol kg}^{-1}$

Match with the asked form

The question asks: $\underline{\hspace{1cm}} \times 10^{-3}\,m$

Since $0.16419 = 164.19 \times 10^{-3}$

Nearest integer $= 164$.

Final answer

$\boxed{164}$