Question 13

1. Calculate osmotic pressure ($\pi$) using hydrostatic pressure formula: $\pi = h\rho g$

$h = 2.00\text{ cm} = 0.02\text{ m}$

$\rho = 1.00\text{ g cm}^{-3} = 1000\text{ kg m}^{-3}$

$g = 10\text{ m s}^{-2}$

$\pi = 0.02 \times 1000 \times 10 = 200\text{ Pa (or N m}^{-2})$

2. Use the osmotic pressure formula $\pi = CRT$ where $C$ is molar concentration:

$\pi = \frac{w}{MV}RT$

Given mass concentration $\frac{w}{V} = 2.00\text{ g dm}^{-3} = 2.00\text{ g/L} = 2000\text{ g m}^{-3}$

$200 = \frac{2000}{M} \times 8.3 \times 300$

$M = \frac{2000 \times 8.3 \times 300}{200}$

$M = 10 \times 2490 = 24900\text{ g mol}^{-1}$

$M = 2.49 \times 10^4\text{ g mol}^{-1}$

Therefore, $X = 2.49$.