Osmotic pressure of a solution is 0.0821 atm at temperature of 300 K. The concentration of solution in moles/litre will be

Options

A. `0.33`
B. `0.066`
C. `0.3xx10^(-2)`
D. `3`

Explanation

To find the concentration of the solution in moles per liter (M), we can use the formula for osmotic pressure:

\[ \Pi = CRT \]

Where:
- \(\Pi\) = osmotic pressure (in atm)
- \(C\) = concentration (in moles per liter)
- \(R\) = ideal gas constant (0.0821 L·atm/(K·mol))
- \(T\) = temperature (in Kelvin)

Given:
- \(\Pi = 0.0821 \, \text{atm}\)
- \(T = 300 \, \text{K}\)
- \(R = 0.0821 \, \text{L·atm/(K·mol)}\)

**Step 1: Rearranging the formula to find concentration (C)**

We can rearrange the formula to solve for \(C\):

\[ C = \frac{\Pi}{RT} \]

**Step 2: Substituting the values into the equation**

Now, we substitute the known values into the equation:

\[ C = \frac{0.0821 \, \text{atm}}{(0.0821 \, \text{L·atm/(K·mol)}) \times (300 \, \text{K})} \]

**Step 3: Calculating the denominator**

Calculating the denominator:

\[ RT = 0.0821 \, \text{L·atm/(K·mol)} \times 300 \, \text{K} = 24.63 \, \text{L·atm/mol} \]

**Step 4: Completing the calculation for concentration (C)**

Now, we can calculate \(C\):

\[ C = \frac{0.0821 \, \text{atm}}{24.63 \, \text{L·atm/mol}} \approx 0.00334 \, \text{mol/L} \]

Thus, the concentration of the solution is approximately:

\[ C \approx 0.00334 \, \text{mol/L} \]