A solution contains non-volatile solute of molecular mass `M_p`. Which of the following can be used to calculate molecular mass of the solute in terms of osmotic pressure (m = Mass of solute, V = Volume of solution and `pi` = Osmotic pressure)

Options

A. `Mp=(m/pi)VRT`
B. `Mp=(m/V)(RT)/pi`
C. `Mp=(m/V)pi/(RT)`
D. `Mp=(m/V)piRT`

Answer

To calculate the molecular mass of a non-volatile solute in terms of osmotic pressure, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the relationship of osmotic pressure**:
The osmotic pressure (π) of a solution can be expressed using the formula:
\[ \pi = i \cdot C \cdot R \cdot T \]
where:
- \( \pi \) = osmotic pressure
- \( i \) = van 't Hoff factor (which is 1 for non-volatile, non-electrolyte solutes)
- \( C \) = concentration of the solution in moles per liter (mol/L)
- \( R \) = universal gas constant
- \( T \) = temperature in Kelvin

2. **Substituting for non-volatile solute**:
Since the solute is non-volatile and does not dissociate, we can simplify the equation to:
\[ \pi = C \cdot R \cdot T \]

3. **Express concentration (C)**:
The concentration \( C \) can be defined in terms of the mass of the solute (m) and its molecular mass (M_p):
\[ C = \frac{n}{V} \]
where \( n \) is the number of moles of solute and \( V \) is the volume of the solution. The number of moles \( n \) can be expressed as:
\[ n = \frac{m}{M_p} \]
Thus, we can rewrite concentration as:
\[ C = \frac{m}{M_p \cdot V} \]

4. **Substituting concentration back into the osmotic pressure equation**:
Now, substituting this expression for \( C \) into the osmotic pressure equation gives:
\[ \pi = \left(\frac{m}{M_p \cdot V}\right) \cdot R \cdot T \]

5. **Rearranging to solve for molecular mass (M_p)**:
To find \( M_p \), we can rearrange the equation:
\[ M_p = \frac{m \cdot R \cdot T}{\pi \cdot V} \]

### Final Expression:
Thus, the molecular mass \( M_p \) of the solute can be calculated using the formula:
\[ M_p = \frac{m \cdot R \cdot T}{\pi \cdot V} \]

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