Question

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

The molar mass of catalase is approximately \(2.52 * 10^5 \mathrm{~g/mol}\).

Step-by-step solution

Convert temperature to Kelvin and pressure to atm

First, we need to convert the given temperature of 27°C to Kelvin. We do this by adding 273.15. T = 27 + 273.15 = 300.15 K Next, we need to convert the osmotic pressure from torr to atm. We use the conversion factor: 1 atm = 760 torr Π = 0.745 torr * (1 atm / 760 torr) = 0.0009796 atm

Rearrange the osmotic pressure formula to find the number of moles (n)

Now we will rearrange the osmotic pressure formula to find the number of moles (n): n = (Π * V) / (R * T) Where V is the volume (1.00 L), R is the ideal gas constant (0.0821 L atm/mol K), and T is the temperature (300.15 K).

Calculate the number of moles (n) of catalase

Now plug in the values for Π, V, R, and T to calculate the number of moles: n = (0.0009796 atm * 1.00 L) / (0.0821 L atm/mol K * 300.15 K) n ≈ 3.97 * 10^-5 mol

Calculate the molar mass (M) of catalase

Now that we have the number of moles, we can find the molar mass (M) of catalase using the formula: M = mass / n Where mass is the mass of catalase (10.00 g) and n is the number of moles (3.97 * 10^-5 mol). M = 10.00 g / (3.97 * 10^-5 mol) ≈ 2.52 * 10^5 g/mol The molar mass of catalase is approximately 2.52 * 10^5 g/mol.