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What is the molar mass of the unknown protein if a solution containing 37.1 mg of the protein in 82.0 mL of solution exhibits an osmotic pressure of 3.91 mmHg at 35.7 °C?

Answer :

Final answer:

The molar mass of the unknown protein is approximately 217 grams per mole (g/mol).

Explanation:

To find the molar mass of the unknown protein, you can use the formula for osmotic pressure and rearrange it to solve for the molar mass:

π = (n/V)RT

Where:

  • π = osmotic pressure (in atm)
  • n = moles of solute
  • V = volume of solution (in liters)
  • R = ideal gas constant (0.0821 L.atm/(mol.K))
  • T = temperature (in Kelvin)

First, you need to convert the given temperature from Celsius to Kelvin:

T = 35.7°C + 273.15 = 308.85 K

Next, convert the osmotic pressure from mmHg to atm:

π = 3.91 mmHg / 760 mmHg/atm ≈ 0.005145 atm

Now, you can calculate the moles of solute (protein) using the given mass and volume:

Mass of protein (m) = 37.1 mg = 0.0371 g

Volume of solution (V) = 82.0 ml = 0.0820 L

Now, we can calculate moles of protein (n):

n = (0.0371 g) / (molar mass of protein)

Now, plug the values into the osmotic pressure equation:

0.005145 atm = (n / 0.0820 L) * (0.0821 L.atm/(mol.K)) * 308.85 K

Solve for n:

n = (0.005145 atm * 0.0820 L) / (0.0821 L.atm/(mol.K) * 308.85 K)

n ≈ 0.0001711 mol

Now that you know the moles of protein, you can solve for the molar mass:

0.0001711 mol = (0.0371 g) / (molar mass of protein)

Rearrange to find the molar mass of the protein:

Molar mass of protein = (0.0371 g) / 0.0001711 mol

Molar mass of protein ≈ 217 g/mol

So, the molar mass of the unknown protein is approximately 217 grams per mole (g/mol).

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