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Chapter 13: Problem 104

A mixture of \(\mathrm{NaCl}\) and sucrose \(\left(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\right)\) of combined mass \(10.2 \mathrm{~g}\) is dissolved in enough water to make up a \(250 \mathrm{~mL}\) solution. The osmotic pressure of the solution is \(7.32 \mathrm{~atm}\) at \(23^{\circ} \mathrm{C}\). Calculate the mass percent of \(\mathrm{NaCl}\) in the mixture.

Short Answer

Expert verified
The mass percent of NaCl in the mixture is approximately 38.92%.

Step by step solution

01

Decompose the given

First, let's break down what we have: the total combined mass of the NaCl and sucrose in the mixture is 10.2 g and they are dissolved in enough water to make up a 250 mL solution. The osmotic pressure exerted by these dissolved particles is shown to be 7.32 atm at a temperature of 23 degrees Celsius. Note that we want to find out what portion of that 10.2 g is NaCl.
02

Use the osmotic pressure formula

The osmotic pressure (P) formula is derived from the ideal gas law, and given by P= nRT/V, where n is the number of moles, R is the universal gas constant (0.0821 L.atm/K.mol), T is the absolute temperature in Kelvin, and V is volume in liters. Since P= nRT/V, we can derive the formula to solve for n=PV/RT. Use this formula to compute the total number of moles of both the NaCl and sucrose.
03

Convert temperature from Celsius to Kelvin

The absolute temperature T in the formula needs to be in Kelvin. Convert the given temperature from Celsius to Kelvin by adding 273.15 to the Celsius temperature. So T = 23 + 273.15 = 296.15 K.
04

Convert volume from mL to L

The volume V in the formula needs to be in liters. Convert the given volume from mL to L by dividing by 1000. So V = 250/1000 = 0.25 L.
05

Calculate the total moles

Now everything is in proper units, so we can compute the total number of moles (n) = PV/RT = (7.32)(0.25)/(0.0821)(296.15) ≈ 0.075 mol
06

Determine the mass of NaCl and sucrose

Assume that x is the mass (in g) of NaCl in the solution and (10.2 - x) is the mass (in g) of sucrose in solution. Given the molar masses of NaCl (58.44 g/mol) and sucrose (342.3 g/mol), we can express the number of moles of each as n= mass/molar mass. So, for NaCl, the moles are x/58.44, and for sucrose, the moles are (10.2 - x)/342.3.
07

Solve for the mass of NaCl

Since the total moles are equal to the moles of NaCl plus the moles of sucrose, we can write the equation 0.075 = x/58.44 + (10.2 - x)/342.3. Solving this equation for x, we find that x ≈ 3.97 g.
08

Calculate the mass percent of NaCl

The mass percent is the mass of the NaCl (x) divided by the total mass of the mixture (10.2 g), multiplied by 100. So, mass percent = (x/10.2)*100 = (3.97/10.2)*100 ≈ 38.92%

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Most popular questions from this chapter

In each case, indicate which of these pairs of compounds is more likely to form ion pairs in water: (a) \(\mathrm{NaCl}\) or \(\mathrm{Na}_{2} \mathrm{SO}_{4}\) (b) \(\mathrm{MgCl}_{2}\) or \(\mathrm{MgSO}_{4},\) (c) \(\mathrm{LiBr}\) or \(\mathrm{KBr}\)

Liquids A (molar mass \(100 \mathrm{~g} / \mathrm{mol}\) ) and \(\mathrm{B}\) (molar mass \(110 \mathrm{~g} / \mathrm{mol}\) ) form an ideal solution. At \(55^{\circ} \mathrm{C}\), A has a vapor pressure of \(95 \mathrm{mmHg}\) and \(\mathrm{B}\) has a vapor pressure of \(42 \mathrm{mmHg}\). A solution is prepared by mixing equal masses of \(\mathrm{A}\) and \(\mathrm{B}\). (a) Calculate the mole fraction of each component in the solution. (b) Calculate the partial pressures of \(\mathrm{A}\) and \(\mathrm{B}\) over the solution at \(55^{\circ} \mathrm{C}\). (c) Suppose that some of the vapor described in (b) is condensed to a liquid. Calculate the mole fraction of each component in this liquid and the vapor pressure of each component above this liquid at \(55^{\circ} \mathrm{C}\).

Explain why ethanol \(\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\right)\) is not soluble in cyclohexane \(\left(\mathrm{C}_{6} \mathrm{H}_{12}\right) .\)

What is osmosis? What is a semipermeable membrane?

A \(3.20-\mathrm{g}\) sample of a salt dissolves in \(9.10 \mathrm{~g}\) of water to give a saturated solution at \(25^{\circ} \mathrm{C}\). What is the solubility (in \(\mathrm{g}\) salt/ \(100 \mathrm{~g}\) of \(\mathrm{H}_{2} \mathrm{O}\) ) of the salt?
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