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Chapter 11: Problem 124

A \(4.7 \times 10^{-2}\) mg sample of a protein is dissolved in water to make 0.25 \(\mathrm{mL}\) of solution. The osmotic pressure of the solution is 0.56 torr at \(25^{\circ} \mathrm{C}\) . What is the molar mass of the protein?

Short Answer

Expert verified
The molar mass of the protein is approximately \(4.66 \times 10^3 \mathrm{g/mol}\).

Step by step solution

01

Write down the osmotic pressure formula

The osmotic pressure formula is given by: \[\Pi = \cfrac{nRT}{V}\] Where: \(\Pi\) = osmotic pressure, \(n\) = number of moles of solute, \(R\) = gas constant, \(T\) = temperature in Kelvin, and \(V\) = volume of the solution.
02

Convert temperature to Kelvin

We know that the temperature is given in Celsius, and we need to convert it to Kelvin. To do this, add 273.15 to the given temperature: \[T = 25 + 273.15 = 298.15 \mathrm{K}\]
03

Convert torr to atmosphere

The osmotic pressure is given in torr, we need to convert it to atmosphere (atm), because the gas constant R is in atm when used for osmotic pressure calculations. Use the conversion factor 1 atm = 760 torr: \[\Pi = \cfrac{0.56 \mathrm{torr}}{760 \mathrm{torr/atm}} = 7.37 \times 10^{-4} \mathrm{atm}\]
04

Convert volume to liters

The volume is given in mL, we need to convert it to liters to work with the osmotic pressure formula. Use the conversion factor 1 L = 1000 mL: \[V = \cfrac{0.25 \mathrm{mL}}{1000 \mathrm{mL/L}} = 2.50 \times 10^{-4} \mathrm{L}\]
05

Find the number of moles

Use the osmotic pressure formula to find the number of moles of the protein: \[n = \cfrac{\Pi V}{RT}\] Where: \(R\) = 0.0821 \(\mathrm{L\cdot atm / (mol\cdot K)}\), Plug in the values of \(\Pi\), \(T\), and \(V\) we found earlier: \[n = \cfrac{7.37 \times 10^{-4} \mathrm{atm} \times 2.50 \times 10^{-4} \mathrm{L}}{0.0821 \mathrm{L\cdot atm / (mol\cdot K)} \times 298.15 \mathrm{K}} = 1.01 \times 10^{-5} \mathrm{mol}\]
06

Calculate molar mass

We are given the mass of the protein sample in mg, so we will first convert it to grams using the conversion factor 1 g = 1000 mg: \[m = 4.7 \times 10^{-2} \mathrm{mg} \times \cfrac{1\mathrm{g}}{1000\mathrm{mg}} = 4.7 \times 10^{-5} \mathrm{g}\] Then, we can use the number of moles we found in step 5 to calculate the molar mass of the protein: \[M = \cfrac{m}{n} = \cfrac{4.7 \times 10^{-5} \mathrm{g}}{1.01 \times 10^{-5} \mathrm{mol}} = 4.66 \times 10^3 \mathrm{g/mol}\] The molar mass of the protein is approximately \(4.66 \times 10^3 \mathrm{g/mol}\).

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Most popular questions from this chapter

Which ion in each of the following pairs would you expect to be more strongly hydrated? Why? a. \(\mathrm{Na}^{+}\) or \(\mathrm{Mg}^{2+}\) b. \(\mathrm{Mg}^{2+}\) or \(\mathrm{Be}^{2+}\) c. \(\mathrm{Fe}^{2+}\) or \(\mathrm{Fe}^{3+}\) d. \(\mathrm{F}^{-}\) or \(\mathrm{Br}^{-}\) e. \(\mathrm{Cl}^{-}\) or \(\mathrm{ClO}_{4}^{-}\) f. \(\mathrm{ClO}_{4}^{-}\) or \(\mathrm{SO}_{4}^{2-}\)

If a solution shows positive deviations from Raoult’s law, would you expect the solution to have a higher or lower boiling point than if it were ideal? Explain.

Specifications for lactated Ringer’s solution, which is used for intravenous (IV) injections, are as follows to reach 100. mL of solution: \(285-315 \mathrm{mg} \mathrm{Na}^{+}\) \(14.1-17.3 \mathrm{mg} \mathrm{K}^{+}\) \(4.9-6.0 \mathrm{mg} \mathrm{Ca}^{2+}\) \(368-408 \mathrm{mg} \mathrm{Cl}^{-}\) \(231-261 \mathrm{mg}\) lactate, $\mathrm{C}_{3} \mathrm{H}_{5} \mathrm{O}_{3}^{-}$ a. Specify the amount of $\mathrm{NaCl}, \mathrm{KCl}, \mathrm{CaCl}_{2} \cdot 2 \mathrm{H}_{2} \mathrm{O},\( and \)\mathrm{NaC}_{3} \mathrm{H}_{5} \mathrm{O}_{3}\( needed to prepare \)100 . \mathrm{mL}$ lactated Ringer's solution. b. What is the range of the osmotic pressure of the solution at $37^{\circ} \mathrm{C},$ given the preceding specifications?

The normal boiling point of diethyl ether is \(34.5^{\circ} \mathrm{C}\) . A solution containing a nonvolatile solute dissolved in diethyl ether has a vapor pressure of 698 torr at \(34.5^{\circ} \mathrm{C} .\) What is the mole fraction of diethyl ether in this solution?

a. Use the following data to calculate the enthalpy of hydration for calcium chloride and calcium iodide. $$\begin{array}{lll}{\mathrm{CaCl}_{2}(s)} & {-2247 \mathrm{k} / \mathrm{mol}} & {-46 \mathrm{kJ} / \mathrm{mol}} \\ {\mathrm{Cal}_{2}(s)} & {-2059 \mathrm{k} / \mathrm{mol}} & {-104 \mathrm{kJ} / \mathrm{mol}}\end{array}$$ b. Based on your answers to part a, which ion, \(\mathrm{Cl}^{-}\) or \(\mathrm{I}^{-},\) is more strongly attracted to water?
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