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Chapter 13: Problem 81

Lysozyme is an enzyme that breaks bacterial cell walls. A solution containing \(0.150 \mathrm{~g}\) of this enzyme in \(210 \mathrm{~mL}\) of solution has an osmotic pressure of \(0.127 \mathrm{kPa}\) at \(25^{\circ} \mathrm{C}\). What is the molar mass of lysozyme?

Short Answer

Expert verified
The molar mass of lysozyme is approximately \(13.89 \frac{\mathrm{g}}{\mathrm{mol}}\).

Step by step solution

01

Write down the given information

We have the following information: - Mass of lysozyme: \(0.150 \mathrm{~g}\) - Volume of the solution: \(210 \mathrm{~mL}\) - Osmotic pressure: \(0.127 \mathrm{kPa}\) - Temperature: \(25^{\circ} \mathrm{C}\)
02

Convert the given information to appropriate units

We need to convert the temperature to Kelvin and the volume of the solution to liters: - Temperature in Kelvin: \(25^{\circ} \mathrm{C} + 273.15 = 298.15 \mathrm{K}\) - Volume of the solution in liters: \(\frac{210 \mathrm{~mL}}{1000} = 0.210 \mathrm{~L}\)
03

Use the osmotic pressure equation to solve for molar concentration

The osmotic pressure equation is given by: \(Π = \frac{n}{V} \times R \times T\) Where: - \(Π\) is the osmotic pressure - \(n\) is the number of moles of solute - \(V\) is the volume of the solution - \(R\) is the ideal gas constant (\(R = 8.314 \frac{\mathrm{J}}{\mathrm{mol \cdot K}}\)) - \(T\) is the temperature in Kelvin We can solve for the number of moles, \(n\), by re-arranging the equation: \(n = \frac{Π \times V}{R \times T}\) Now plug in the given values: \(n = \frac{0.127 \times 10^3 \times 0.210}{8.314 \times 298.15}\) \(n \approx 0.01080 \mathrm{~mol}\)
04

Calculate the molar mass

Now that we have the number of moles, we can calculate the molar mass by dividing the mass of lysozyme by the moles: Molar mass = \(\frac{mass}{moles}\) Molar mass = \(\frac{0.150 \mathrm{~g}}{0.01080 \mathrm{~mol}}\) Molar mass \(\approx 13.89 \frac{\mathrm{g}}{\mathrm{mol}}\) The molar mass of lysozyme is approximately \(13.89 \frac{\mathrm{g}}{\mathrm{mol}}\).

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Most popular questions from this chapter

Commercial aqueous nitric acid has a density of $1.12 \mathrm{~g} / \mathrm{mL}\( and is 3.7 M. Calculate the percent \)\mathrm{HNO}_{3}$ by mass in the solution.

Indicate whether each statement is true or false: (a) If you compare the solubility of a gas in water at two different temperatures, you find the gas is more soluble at the lower temperature. (b) The solubility of most ionic solids in water decreases as the temperature of the solution increases. (c) The solubility of most gases in water decreases as the temperature increases because water is breaking its hydrogen bonding to the gas molecules as the temperature is raised. (d) Some ionic solids become less soluble in water as the temperature is raised.

List the following aqueous solutions in order of increasing boiling point: \(0.080 \mathrm{~m} \mathrm{KBr}, 0.130 \mathrm{~m}\) urea \(\left(\mathrm{CO}\left(\mathrm{NH}_{2}\right)_{2}\right)\), $0.080 \mathrm{~m} \mathrm{Mg}\left(\mathrm{NO}_{2}\right)_{2}\( \)0.030 \mathrm{~m}$ phenol \(\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{OH}\right)\)

Consider two ionic solids, both composed of singly charged ions, that have different lattice energies. (a) Will the solids have the same solubility in water? (b) If not, which solid will be more soluble in water, the one with the larger lattice energy or the one with the smaller lattice energy? Assume that solute-solvent interactions are the same for both solids. [Section 13.1]

Would you expect alanine (an amino acid) to be more soluble in water or in hexane?
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