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 \(2.41 \times 10^5 \mathrm{g/mol}\).

Step by step solution

01

Convert the temperature to Kelvin and pressure to atm

First, we need to convert the given temperature from Celsius to Kelvin: \( T (K) = T ( °C) + 273.15 \) Next, we need to convert the osmotic pressure from torr to atm: 1 atm = 760 torr
02

Calculate the molar concentration of catalase

Equating the osmotic pressure formula, we get: Osmotic Pressure = (Molar Concentration) × (R) × (Temperature in K) Rearranging to find Molar Concentration: Molar Concentration = (Osmotic Pressure) / (R × Temperature in K) Now, substitute the given values and the converted values from Step 1 into the equation and solve for the molar concentration: R (ideal gas constant) = 0.0821 L atm / (K mol)
03

Find the number of moles of catalase

Using the calculated molar concentration and the volume of the solution, we can find the number of moles of catalase: Number of moles of catalase = (Molar Concentration) × (Volume of solution in L)
04

Calculate the molar mass of catalase

Finally, we can use the formula for molar mass to find the molar mass of catalase: Molar Mass = (mass of solute) / (number of moles of solute) Now, substitute the values obtained from Steps 2 and 3 into the formula and find the molar mass of catalase.

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