   Chapter 13.1, Problem 13.1CYU

Chapter
Section
Textbook Problem

(a) If you dissolve 10.0 g (about one heaping teaspoonful) of sugar (sucrose, C12H22O11) in a cup of water (250. g), what are the mole fraction, molality, and weight percent of sugar? (b) Seawater has a sodium ion concentration of 1.08 × 104 ppm. If the sodium is present in the form of dissolved sodium chloride, what mass of NaCl is in each liter of seawater? Seawater is denser than pure water because of dissolved salts. Its density is 1.05 g/mL

(a)

Interpretation Introduction

Interpretation: The mole fraction, molality, and weight percent of sugar has to be identified.

Concept introduction:

Mole fraction: Amount of that component divided by the total amount of all of the components of the mixture ( nA +  nB +  n...).

Mole fraction of A (χA)= nA nA +  nB +  n...

Molality: The amount of solute (mol) per kilogram of solvent.

Concentration (C, mol/kg) =  molality of solute = Amount of solute (mol)Mass of solvent (Kg)

Weight percent: The mass of one component divided by the total mass of the mixture, multiplied by 100%

weight % A = Mass of A Mass of A + Mass of B + Mass of C + ...×100%

Explanation

Given data:

Sucrose = 10.0 g  water = 250 g

• The Mole fraction:

No.ofmoles=massmolarmass

no.of moles (sucrose) = 10 g 342.3 g/mol = 0.030 molno.of moles (Water) = 250 g 18 g/mol = 13.9 mol

Mole fraction is the amount of that component divided by the total amount of all of the components of the mixture ( nA +  nB +  n...).

Mole fraction of A (χA)= nA nA +  nB +  n...

nsucrose= 0.030 molnWater= 13.9 molMole fraction : (χsucrose) = nsucrose nsucrose +  nWater  = 0.030 mol0.030 mol + 13.9 mol = 0.00210

Convert the mass of glycol and water into unit of moles and substitute in the respective mole fraction equation as shown above. Hence, the mole fraction of ethylene glycol is 0.00210

• The molality:

Given data:

Sucrose = 10

b)

Interpretation Introduction

Interpretation: The mass of sodium chloride has to be determined.

Concept introduction:

An important measure of concentration is ppm

mg/L=ppm

1mgL=0.001g1000mL=0.001g1000cm3=1g106g

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