Lysozyme is an enzyme that cleaves bacterial cell walls. A sample of lysozyme ex

Question

Lysozyme is an enzyme that cleaves bacterial cell walls. A sample of lysozyme extracted from egg white has a molar mass of 13,930 g. A quantity of 0.200 g of this enzyme is dissolved in 1.40 x 102g of water at 25°c. Calculate the vapor-pressure lowering, the depression in freezing point, the elevation in boiling point, and the osmotic pressure of this solution. (The vapor pressure of water at 25°C is 23.76 mmHg.) Report each of your answers to 3 significant figures. Vapor-pressure lowering mmHg n in freezing point- Elevation in boiling point = Osmotic pressure- atm

Explanation / Answer

Mass of solute = 0.200 g.

Molar mass if solute = 13930 g/mol

Moles of solute = mass / molar mass = 0.200 / 13930 = 0.0000144 mol

Mass of water = 140 g.

Molality = moles of solute / mass of solvent in kg

m = 0.0000144 / 0.140 = 0.000102 m

Vapour pressure of pure solvent = 23.76 mmHg

Moles of solvent = 140 / 18 = 7.78 mol

Mole fraction of solute = moles of solute / total moles of solution

Xsolute = 0.0000144 / ( 0.0000144 + 7.78) = 0.00000185

Kf of water = 1.86

Kb of water = 0.512

NOW.

1.

(po - p) / p0 = Xsolute

( p0 - p) / 23.76 = 0.00000185

p0 - p = vapour pressure lowering = 0.0000440 mmHg

p = vapour pressure of solution = 23.76 - 0.0000440

p = 23.76 ( approx.)

2.

Depression in freezing point = Kf * m = 1.86 * 0.000102 = 0.000190 degree C

3.

Elevation in boiling point = Kb * m = 0.512 * 0.000102=0.0000522 degree C

4.

Osmotic pressure = C R T = 0.000102 * 0.0821 * 298.15 = 0.00250 atm

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