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Chapter 13: Problem 81

Lysozyme is an enzyme that breaks bacterial cell walls. A solution containing 0.150 gof this enzyme in 210 \(\mathrm{mL}\) of solution has an osmotic pressure of 0.953 torr at \(25^{\circ} \mathrm{C}\) . What is the molar mass of lysozyme?

Short Answer

Expert verified
The molar mass of lysozyme is approximately 13,898.22 g/mol.

Step by step solution

01

Convert the temperature to Kelvin

Given the temperature is 25°C, we need to convert it to Kelvin by adding 273.15 to it. \(T(K) = 25 + 273.15 = 298.15\ K\)
02

Convert osmotic pressure to atm

The osmotic pressure is given in torr. We need to convert it to atm (the unit for the ideal gas constant R). 1 atm = 760 torr, therefore: \(\pi(atm) = \dfrac{0.953 \ torr}{760 \ torr/atm} = 0.001254 \ atm\)
03

Use the osmotic pressure equation

Rearrange the osmotic pressure equation to get the concentration: \((concentration) = \dfrac{\pi}{R \times T}\) Plug in the osmotic pressure, temperature, and the ideal gas constant (R = 0.0821 L atm/mol K): \((concentration) = \dfrac{0.001254 \ atm}{0.0821 \ L \ atm/mol \ K \times 298.15 \ K} = 5.14 \times 10^{-5} \ mol/L\)
04

Determine the moles of lysozyme

The volume of the solution is given in milliliters (210 mL). Convert it to liters: \(V = \dfrac{210 \ mL}{1000 \ mL/L} = 0.21\ L\) Now, find the moles of lysozyme using the concentration: \((moles) = (concentration) \times (volume) = 5.14 \times 10^{-5} \ mol/L \times 0.21 \ L = 1.08 \times 10^{-5} \ mol\)
05

Calculate the molar mass

Now that we have the moles of lysozyme, we can calculate its molar mass. We are given that the mass of lysozyme is 0.150 g. Use the relationship: \(Molar \ mass = \dfrac{mass}{moles}\) Plug in the values: \(Molar \ mass = \dfrac{0.150 \ g}{1.08 \times 10^{-5} \ mol} = 13898.22 \ g/mol\) So, the molar mass of lysozyme is approximately 13,898.22 g/mol.

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Most popular questions from this chapter

A solution is made containing 20.8 \(\mathrm{g}\) of phenol \(\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{OH}\right)\) in 425 \(\mathrm{g}\) of ethanol \(\left(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}\right) .\) Calculate (a) the mole fraction of phenol, ( b) the mass percent of phenol, (c) the molality of phenol.

The partial pressure of \(\mathrm{O}_{2}\) in air at sea level is 0.21 atm. Using the data in Table \(13.1,\) together with Henry's law, calculate the molar concentration of \(\mathrm{O}_{2}\) in the surface water of a mountain lake saturated with air at \(20^{\circ} \mathrm{C}\) and an atmospheric pressure of 650 torr.

Suppose you had a balloon made of some highly flexible semipermeable membrane. The balloon is filled completely with a 0.2\(M\) solution of some solute and is submerged in a 0.1 \(\mathrm{M}\) solution of the same solute: Initially, the volume of solution in the balloon is 0.25 L. Assuming the volume outside the semipermeable membrane is large, as the illustration shows, what would you expect for the solution volume inside the balloon once the system has come to equilibrium through osmosis? [Section 13.5\(]\)

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A "canned heat" product used to warm buffet dishes consists of a homogeneous mixture of ethanol \(\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\right)\) and paraffin, which has an average formula of \(\mathrm{C}_{24} \mathrm{H}_{50}\). What mass of \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\) should be added to \(620 \mathrm{~kg}\) of the paraffin to produce 8 torr of ethanol vapor pressure at \(35^{\circ} \mathrm{C}\) ? The vapor pressure of pure ethanol at \(35^{\circ} \mathrm{C}\) is 100 torr.
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