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Chapter 11: Problem 75

An aqueous solution of \(10.00 \mathrm{~g}\) of catalase, an enzyme found in the liver, has a volume of \(1.00 \mathrm{~L}\) at \(27^{\circ} \mathrm{C}\). The solution's osmotic pressure at \(27^{\circ} \mathrm{C}\) is found to be \(0.745\) torr. Calculate the molar mass of catalase.

Short Answer

Expert verified
The molar mass of catalase is approximately \(250,500 \mathrm{~g/mol}\).

Step by step solution

01

Convert temperature to Kelvin

First, convert the temperature from Celsius to Kelvin using the formula: K = °C + 273.15 T = 27°C + 273.15 = 300.15 K
02

Convert osmotic pressure to atm

Next, convert the osmotic pressure from torr to atm using the conversion factor: 1 atm ≈ 760 torr Π = 0.745 torr × (1 atm / 760 torr) ≈ 0.00098026 atm
03

Rewrite osmotic pressure formula

We can rewrite the osmotic pressure formula to find the number of moles (n) of solute: n = ΠV/RT
04

Find the number of moles of solute

Now, we can substitute the known values into the formula to find the number of moles of catalase: n = (0.00098026 atm)(1.00 L) / (0.08206 L·atm/mol·K)(300.15 K) ≈ 3.996 × 10⁻⁵ mol
05

Calculate molar mass of catalase

To find the molar mass of catalase, divide the mass of catalase by the number of moles: Molar mass = (10.00 g) / (3.996 × 10⁻⁵ mol) ≈ 250,500 g/mol So, the molar mass of catalase is approximately 250,500 g/mol.

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