Question

A 226 mL solution containing 22 g of a protein in toluene has an osmotic pressure of 0.053 atm at 27 oC. What is the molar mass (in g/mol) of the protein

Answer 1

Answer:

4.4 × 10⁴ g/mol

Explanation:

The osmotic pressure (π) is a colligative property that can be calculated using the following expression.

π = M × R × T

where,

M: molarity

R: ideal gas constant

T: absolute temperature (27°C + 273.15 = 300 K)

Let's use it to find the molarity of the protein.

M = π / R × T

M = 0.053 atm / (0.082 atm.L/mol.K) × 300 K

M = 2.2 × 10⁻³ M

The molarity of the protein is:

M = mass of the protein / molar mass of the protein × liters of solution

molar mass of the protein = mass of the protein / M  × liters of solution

molar mass of the protein = 22 g / 2.2 × 10⁻³ mol/L  × 0.226 L

molar mass of the protein = 4.4 × 10⁴ g/mol

Answer 2

The molar mass of the protein is 4.4 * 10⁴ g/mol

Osmotic pressure :

It  is a colligative property that can be calculated using the following expression.

π = M × R × T

where,

• M= molarity
• R= ideal gas constant
• T= absolute temperature (27°C + 273.15 = 300 K)

• Calculation for the molarity of the protein.

$M = \frac{\pi}{R * T} \\\\M = \frac{0.053 atm}{(0.082 atm.L/mol.K) * 300 K}\\\\ M = 2.2 * 10^{-3} M$

• The molarity of the protein is:

M = mass of the protein / Molar mass of the protein * liters of solution

Molar mass of the protein = mass of the protein / M  * liters of solution

Molar mass of the protein = $\frac{22 g}{2.2 * 10^{-3} mol/L * 0.226 L}$

Molar mass of the protein = $4.4 * 10^4 g/mol$

Thus, the molar mass of the protein is 4.4 * 10⁴ g/mol.

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