/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 77 Lysozyme is an enzyme that break... [FREE SOLUTION] | 91影视

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Chapter 13: Problem 77

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 \(0.953\) torr at \(25^{\circ} \mathrm{C}\). What is the molar mass of lysozyme?

Short Answer

Expert verified
The molar mass of lysozyme is approximately \(14053 ~g/mol\).

Step by step solution

01

Write down the given information

- Mass of lysozyme: \(0.150~g\) - Volume of solution: \(210~mL\) - Osmotic pressure: \(0.953~torr\) - Temperature: \(25^{\circ}C\)
02

Convert the given units to their appropriate units

We need to convert the given units to their appropriate units to use the osmotic pressure formula. We will convert the volume of the solution to liters and the osmotic pressure to atmospheres. - Volume of solution: \(210~mL = 0.210~L\) - Osmotic pressure: \(0.953~torr 脳 \frac{1 ~atm}{760 ~torr} = 0.001253~atm\) We also need to convert the temperature to Kelvin: - Temperature: \(25^{\circ}C + 273.15 = 298.15~K\)
03

Use the osmotic pressure formula to calculate the molarity

The formula for osmotic pressure is given by: \(螤 = MRT\), where \(螤\) is the osmotic pressure, \(M\) is the molarity, \(R\) is the gas constant (\(0.0821 \frac{L\times atm}{mol\times K}\)), and \(T\) is the temperature in Kelvin. Rearrange the formula for molarity: \(M = \frac{螤}{RT}\) Now, substitute the values: \(M = \frac{0.001253~atm}{(0.0821~\frac{L \times atm}{mol \times K})(298.15~K)}\)
04

Calculate the molarity

Calculate the molarity: \(M = 5.086 \times 10^{-5} ~mol/L\)
05

Calculate the molar mass

We have the mass of lysozyme and the molarity. We can now calculate the molar mass using the formula: \(Molar~mass=\frac{mass}{moles}\). We know the moles can be calculated as \(moles = M \times V\), where \(V\) is the volume of the solution. Substitute the values: \(moles = (5.086 \times 10^{-5} ~mol/L)(0.210 ~L) = 1.068 脳 10^{-5}~mol\) Next, calculate the molar mass using the mass of lysozyme and the calculated moles: \(Molar~mass = \frac{0.150~g}{1.068 脳 10^{-5} ~mol} = 14052.91 ~g/mol\) The molar mass of lysozyme is approximately \(14053 ~g/mol\).

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Most popular questions from this chapter

Indicate whether each of the following is a hydrophilic or a hydrophobic colloid: (a) butterfat in homogenized milk, (b) hemoglobin in blood, (c) vegetable oil in a salad dressing, (d) colloidal gold particles in water.

A textbook on chemical thermodynamics states, "The heat of solution represents the difference between the lattice energy of the crystalline solid and the solvation energy of the gaseous ions." (a) Draw a simple energy diagram to illustrate this statement. (b) A salt such as NaBr is insoluble in most polar nonaqueous solvents such as acetonitrile \(\left(\mathrm{CH}_{3} \mathrm{CN}\right)\) or nitromethane \(\left(\mathrm{CH}_{3} \mathrm{NO}_{2}\right)\), but salts of large cations, such as tetramethylammonium bromide \(\left[\left(\mathrm{CH}_{3}\right)_{4} \mathrm{NBr}\right]\), are generally more soluble. Use the thermochemical cycle you drew in part (a) and the factors that determine the lattice energy (Section 8.2) to explain this fact.

(a) Why is there no colloid in which both the dispersed substance and the dispersing substance are gases? (b) Michael Faraday first prepared ruby-red colloids of gold particles in water that were stable for indefinite times. To the unaided eye these brightly colored colloids are not distinguishable from solutions. How could you determine whether a given colored preparation is a solution or colloid?

(a) Calculate the vapor pressure of water above a solution prepared by adding \(22.5 \mathrm{~g}\) of lactose \(\left(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\right)\) to \(200.0 \mathrm{~g}\) of water at \(338 \mathrm{~K}\). (Vapor-pressure data for water are given in Appendix B.) (b) Calculate the mass of propylene glycol \(\left(\mathrm{C}_{3} \mathrm{H}_{8} \mathrm{O}_{2}\right)\) that must be added to \(0.340 \mathrm{~kg}\) of water to reduce the vapor pressure by \(2.88\) torr at \(40^{\circ} \mathrm{C}\).

Ascorbic acid (vitamin \(\mathrm{C}, \mathrm{C}_{6} \mathrm{H}_{8} \mathrm{O}_{6}\) ) is a water-soluble vitamin. A solution containing \(80.5 \mathrm{~g}\) of ascorbic acid dissolved in \(210 \mathrm{~g}\) of water has a density of \(1.22 \mathrm{~g} / \mathrm{mL}\) at \(55^{\circ} \mathrm{C}\). Calculate (a) the mass percentage, (b) the mole fraction, (c) the molality, (d) the molarity of ascorbic acid in this solution.
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