Osmotic pressure is $0.0821 ext{ atm}$ at a temperature of $300 ext{ K}$. Find concentration in mole/litre

Question

Osmotic pressure is $0.0821 	ext{ atm}$ at a temperature of $300 	ext{ K}$. Find concentration in mole/litre:

Accepted Answer

The osmotic pressure ($\Pi$) of a solution is related to its molar concentration ($C$) and temperature ($T$) by the equation: $\Pi = CRT$ .

Given:
*   Osmotic Pressure ($\Pi$) = $0.0821 	ext{ atm}$
*   Temperature ($T$) = $300 	ext{ K}$
*   Gas Constant ($R$) $\approx 0.0821 	ext{ L atm K}^{-1} 	ext{ mol}^{-1}$ (This value is standard for pressure in atm, consistent with the provided data).

Rearranging the formula to solve for concentration ($C$):
$$C = \frac{\Pi}{RT}$$

Substituting the values:
$$C = \frac{0.0821}{0.0821 	imes 300}$$
$$C = \frac{1}{300}$$
$$C \approx 0.00333 	ext{ mol L}^{-1}$$

Converting to scientific notation to match the options:
$$C = 0.33 	imes 10^{-2} 	ext{ mol L}^{-1}$$

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