Arrange the following in increasing order of their osmotic pressure generation at 298 K:
(The cell wall is permeable to water and not to the solute molecules)
(A) If a cell containing 0.5 moles of solute dissolved in 1 L of water is immersed in pure water.
(B) If a cell containing 0.25 moles of solute dissolved in 1 L of water is immersed in pure water.
(C) If a cell containing 0.1 moles of solute dissolved in 0.01 L of water is immersed in pure water.
(D) If a cell containing 0.2 moles of solute dissolved in 0.05 L of water is immersed in pure water.
Choose the correct answer from the options given below:

Question

The plot of osmotic pressure II) vs concentration (mol L^–1 ) for a solution gives a straight line with slope 25.73 L bar mol^–1 . The temperature at which the osmotic pressure measurement is done is
(Use R = 0.083 L bar mol–1 K^–1 )

Answer 1

The osmotic pressure (\( \pi \)) of a solution is calculated using the formula: \( \pi = iCRT \). In this equation:

\( i \) represents the van 't Hoff factor (which is 1 for non-electrolyte solutions).
\( C \) is the molarity of the solution.
\( R \) is the Ideal gas constant, valued at 0.0821 L·atm/mol·K.
\( T \) denotes the temperature in Kelvin.

Given that the temperature and the ideal gas constant remain constant across all scenarios, the osmotic pressure is directly proportional to the molarity of the solution. The molarities for four different cases are calculated as follows:

(A) For a solution with 0.5 moles of solute in 1 L, the molarity is \( C_A = \frac{0.5}{1} = 0.5 \, \text{M}\).
(B) For a solution with 0.25 moles of solute in 1 L, the molarity is \( C_B = \frac{0.25}{1} = 0.25 \, \text{M}\).
(C) For a solution with 0.1 moles of solute in 0.01 L, the molarity is \( C_C = \frac{0.1}{0.01} = 10 \, \text{M}\).
(D) For a solution with 0.2 moles of solute in 0.05 L, the molarity is \( C_D = \frac{0.2}{0.05} = 4 \, \text{M}\).

When these molarities are arranged in ascending order, the sequence is: \( C_B < C_A < C_D < C_C \). Consequently, the solution with the lowest molarity will exhibit the lowest osmotic pressure, and the solution with the highest molarity will exhibit the highest osmotic pressure. Therefore, the order of increasing osmotic pressure is: (B) < (A) < (D) < (C).

The correct order is: (B) < (A) < (D) < (C).

The Correct Option is A

Solution and Explanation

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