   Chapter 2, Problem 160IL

Chapter
Section
Textbook Problem

The “alum” used in cooking is potassium aluminum sulfate hydrate, KAl(SO4)2 · x H2O. To find the value of x, you can heat a sample of the compound to drive off all of the water and leave only KA1(SO4)2. Assume you heat 4.74 g of the hydrated compound and that the sample loses 2.16 g of water. What is the value of x?

Interpretation Introduction

Interpretation: The value of x or the number of water molecules per formula of KAl(SO4)2.xH2O has to be calculated from the given data’s of alum.

Concept introduction:

Moles: One mole is equivalent to the mass of the substance consists same number of units equal to the atoms present in 12g of 12C.

The mole is actually quantity of particles that is Avogadro’s number of particles present in elements or compounds.

The sum of mass of all atoms present in formula of chemical substance is referred as molecular or formula weight of that substance.

Mass: It is the quantitative measure of a substance. The amount of matter present in substance is expressed as mass. The S.I. unit of mass is kg.

Conversion formula for mass of a molecule and number moles,

Numberofmoles=MassingramsMolarmass

Molar mass of a molecule can be calculated from its molecular formula by taking the sum of atomic masses of all the elements present in it.

Explanation

Given,

The mass of hydrated sample KAl(SO4)2.xH2O is 4.74g.

The mass of water molecules in the sample is 2.16g.

The mass of dehydrated sample KAl(SO4)2 is 4.74g2.16g=2.58g.

Equation for finding number moles from mass of a molecule and molar mass is,

Numberofmoles=MassingramsMolarmass

Therefore,

The number of moles of water molecule is,

Numberofmoles=2.16g18g=0

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