Calculate the molecular weight of a substance 10g of which in 1 litre of solution exerts an osmotic pressure of 81 mm Hg at 27K

Answer

To calculate the molecular weight of the substance, we can use the formula for osmotic pressure:

\[ \Pi = \frac{n}{V}RT \]

Where:
- \(\Pi\) = osmotic pressure (in atm)
- \(n\) = number of moles of solute
- \(V\) = volume of solution in liters
- \(R\) = ideal gas constant (0.0821 L·atm/(K·mol))
- \(T\) = temperature in Kelvin

### Step 1: Convert osmotic pressure from mm Hg to atm
To convert the osmotic pressure from mm Hg to atm, we use the conversion factor \(1 \text{ atm} = 760 \text{ mm Hg}\).

\[ \Pi = \frac{81 \text{ mm Hg}}{760 \text{ mm Hg/atm}} = 0.10658 \text{ atm} \]

### Step 2: Convert temperature from Celsius to Kelvin
The temperature given is 27°C. To convert this to Kelvin, we use the formula:

\[ T(K) = T(°C) + 273.15 \]

\[ T = 27 + 273.15 = 300.15 \text{ K} \]

### Step 3: Rearrange the osmotic pressure formula to find the number of moles (n)
We can rearrange the formula to solve for \(n\):

\[ n = \frac{\Pi V}{RT} \]

Substituting the values we have:

\[ n = \frac{0.10658 \text{ atm} \times 1 \text{ L}}{0.0821 \text{ L·atm/(K·mol)} \times 300.15 \text{ K}} \]

Calculating this gives:

\[ n = \frac{0.10658}{24.924} \approx 0.00427 \text{ moles} \]

### Step 4: Calculate the molecular weight (M)
The molecular weight (M) can be calculated using the formula:

\[ M = \frac{mass}{n} \]

Where mass is given as 10 g. Substituting the values:

\[ M = \frac{10 \text{ g}}{0.00427 \text{ moles}} \approx 2341.2 \text{ g/mol} \]

### Final Answer
The molecular weight of the substance is approximately **2341.2 g/mol**.