   Chapter 2, Problem 150GQ

Chapter
Section
Textbook Problem

The elements A and Z combine to produce two different compounds: A2Z3 and AZ2. If 0.15 mol of A2Z3 has a mass of 15.9 g and 0.15 mol of AZ2 has a mass of 9.3 g, what are the atomic weights of A and Z?

Interpretation Introduction

Interpretation: The atomic weights of A and Z are needed to be calculated for the given molecules A2Z3 and AZ2 under given conditions.

Concept introduction:

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

Molarmass=MassingramsNumberofmoles

• 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.
• 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.
• From given mass of substance moles could be calculated by using the following formula,

Molesofsubstance GivenmassofsubstanceMolecularmass

Explanation

Let’s take atomic mass of A and Z as x and y respectively.

The mass and the number of moles of A2Z3 is given that 15.9g and 0.15mol.

The mass and the number of moles of AZ2 is given that 9.3g and 0.15mol.

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

Molarmass=MassingramsNumberofmoles

Therefore,

The molar mass of A2Z3 is,

Molarmass=15.9g0.15mol=106g/mol

The molar mass of AZ2 is,

Molarmass=9.3g0.15mol=62g/mol

The molecule A2Z3 contains 2A and 3Z atoms, so the molar mass of the compound can written as,

2x(atomicmassofA)+3y(

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