   Chapter 3, Problem 193IP

Chapter
Section
Textbook Problem

An iortic compound MX3 is prepared according to the following unbalanced chemical equation. M + X 2 → MX 3 A 0.105-g sample of X2 contains 8.92 × 1020 molecules. The compound MX3 consists of 54.47% X by mass. What are the identities of M and X, and what is the correct name for MX3? Starting with 1.00 g each of M and X2, what mass of MX3 can be prepared?

Interpretation Introduction

Interpretation: The identities of M and X are to be identified. The correct name of MX3 is to be stated. Also, the mass of MX3 is to be calculated.

Concept introduction: The molecular formula of an element defines the total number of atoms present in a molecule. The number of moles is defined as the ratio of mass with the molecular mass of an element. The mass of an element is the amount of the substance present in an element. The mass is calculated by using number of moles in an element.

To determine: The identities M and X, the correct name of MX3 and the mass of MX3 .

Explanation

Explanation

Given

Mass of sample is 0.105 g .

Number of molecules of X2 in a sample is 8.92×1020 molecules.

Mass percent of X in the compound MX3 is 54.47% .

Mass of M is 1.00 g .

Mass of X2 is 1.00 g .

The mass of one mole of X2 is calculated by using the expression,

Mass=Number of moles×Molar mass

For one mole the above expression becomes,

Mass=Number of moles×Molar mass=1×Given MassNumber of molecules×NA

Where,

• NA=6.022×1023 is the Avogadro’s number.

Substitute the value of given mass of sample and number of molecules in the above expression to calculate the mass of one mole of X2 .

Mass=1×Given MassNumber of molecules×NA=1×0.105 g8.92×1020 molecules×6.022×1023 molecules=70.88 g/mol

The mass of X2 is 70.88 g/mol .

Therefore the mass of X is 35.44 g/mol . This is the atomic mass of chlorine. So X2 represents Cl2 .

Mass percent of X in the compound MX3 is 54.47% .

The molar mass of MX3 is considered to be a g/mol.

Since there are three chlorine atoms in a compound, mass of chlorine in MX3 is 3(35.45)=106.35 g .

The molar mass of MX3 is calculated as,

(54.47100)×a=106.35 ga=106.35 g×10054.47 mola=195.24 g/mol

Mass of M is calculated by using the expression,

Mass of M=Mass of MX3Mass of X3

Substitute the value of mass of MX3 and X3 in the above expression to calculate the mass of M

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