What is the molar mass of a solute if a solution prepared by dissolving 0.822 g of it in 300 mdm³ of water has an osmotic pressure of 149 mm Hg at 298 K?

[!NOTE]
The textbook prints the volume as "300 mdm³"; its own solution treats it as 300 mL = 0.3 dm³, and so does ours.

Question

What is the molar mass of a solute if a solution prepared by dissolving 0.822 g of it in 300 mdm³ of water has an osmotic pressure of 149 mm Hg at 298 K?

> [!NOTE]
> The textbook prints the volume as "300 mdm³"; its own solution treats it as 300 mL = 0.3 dm³, and so does ours.

Accepted Answer

> [!TLDR]
> $\pi = 149/760 = 0.196$ atm, V = 0.3 dm³; $M_2 = \dfrac{W_2RT}{\pi V} = 342$ g mol⁻¹.

**Step 1.** Convert the osmotic pressure: $\pi = \dfrac{149}{760} = 0.196$ atm; the volume V = 300 mL = 0.3 dm³ (see the stem note on the book's "300 mdm³").

**Step 2.** From $\pi = \dfrac{W_2RT}{M_2V}$ (Eq. 2.21): $M_2 = \dfrac{W_2RT}{\pi V}$. …

Q.What is the molar mass of a solute if a solution prepared by dissolving 0.822 g of it in 300 mdm³ of water has an osmotic pressure of 149 mm Hg at 298 K?
[!NOTE]
The textbook prints the volume as "300 mdm³"; its own solution treats it as 300 mL = 0.3 dm³, and so does ours.

Concept understanding — Osmotic Pressure

Osmotic Pressure: The Push of Pure Solvent

The Precise Definition

The van't Hoff Equation

Why It Matters for Macromolecules

Q.What is the molar mass of a solute if a solution prepared by dissolving 0.822 g of it in 300 mdm³ of water has an osmotic pressure of 149 mm Hg at 298 K? [!NOTE] The textbook prints the volume as "300 mdm³"; its own solution treats it as 300 mL = 0.3 dm³, and so does ours.

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Q.What is the molar mass of a solute if a solution prepared by dissolving 0.822 g of it in 300 mdm³ of water has an osmotic pressure of 149 mm Hg at 298 K?
[!NOTE]
The textbook prints the volume as "300 mdm³"; its own solution treats it as 300 mL = 0.3 dm³, and so does ours.

Unlock everything free for 14 days