   Chapter 11, Problem 117CWP

Chapter
Section
Textbook Problem

# A solid consists of a mixture of NaNO3 and Mg(NO3)2. When 6.50 g of the solid is dissolved in 50.0 g of water, the freezing point of the solution is lowered by 5.23°C. What is the composition by mass of the solid mixture?

Interpretation Introduction

Interpretation: The mass percentage of Solid mixture has to be calculated.

Concept Introduction:

The mass percentage of a compound is ratio of calculated mass of compound to the total mass whole multiplied by 100. The mass percentage of compound can be given by the equation.

Masspercentage(%)=Calculatedmass(ing)Totalmass(ing)×100

Explanation

Record the given info

Mass of Solid = 6.50g

Mass of Water = 50.0g

Freezing point of the solution = 5.23°C

To calculate the moles of ions in solution

Freezing point depression constant of water = 1.86°C/molal

The moles of ions in the solution is calculated from the molality,

m=ΔTfKf=5.23°C1.86°C/molal=2.81molalTotal ions in solution(n)=2.81molsolutekgsolvent=n0.0500kg=0.141molofionsinsolution

Moles of ions in solution = 0.141mol

To calculate the mass of Sodium nitrate and Magnesium nitrate

Molar mass of Sodium nitrate = 85.00g

Molar mass of Magnesium nitrate = 148.3g

Sodium nitrate and Magnesium nitrate are strong electrolytes,

Let x = mass of Sodium nitrate

y = mass of Magnesium nitrate

0.141molions=2(xmolofNaNO3)+3(ymolMg(NO3)2)6.50g=xmolNaNO3×85.00gmol+ymolMg(NO3)2×148.3gmolTherearetwoequations,2x+3y=0

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