Chapter 7, Problem 61UTC

The chapter sections to review are shown in parentheses at the end of each problem.
Using the models of the molecules (black = C, white = H, yellow = S, green = Cl), determine each of the following for models of compounds 1 and 2: (7.2, 7.4, 7.5, 7.6)

a. molecular formula
c. molar mass
b. empirical formula
d. mass percent composition

Interpretation Introduction

Interpretation: To find the empirical formula of dipyrithione.

Concept Introduction: Empirical formula is the simplest ratio of different elements in a compound.

Answer to Problem 61UTC

The empirical formula of dipyrithione is C₅H₄NOS

Explanation of Solution

The molecular formula of dipyrithione is C₁₀H₈N₂O₂S₂ The subscript of each element is divided by 2. 2 is the minimum number of atoms of elements N, O and S.

  ${\text{C}}_{\frac{10}{2}}{\text{H}}_{\frac{8}{2}}{\text{N}}_{\frac{2}{2}}{\text{O}}_{\frac{2}{2}}{\text{S}}_{\frac{2}{2}}$

Thus the empirical formula is C₅H₄NOS

Interpretation Introduction

Interpretation: To find the molar mass of dipyrithione.

Concept Introduction: Molar mass is found by adding the atomic mass of each element that makes up the compound.

Answer to Problem 61UTC

Molar mass of dipyrithione = 252 g/mol

Explanation of Solution

The molecular formula of dipyrithione is C₁₀H₈N₂O₂S₂ Atomic mass of C = 12 g/mol

Atomic mass of H = 1 g/mol

Atomic mass of N = 14 g/mol

Atomic mass of O = 16 g/mol

Atomic mass of S = 32 g/mol

Molar mass of dipyrithione, C₁₀H₈N₂O₂S₂ = $\text{(12 }\times \text{10) + (1 }\times \text{ 8) + (14 }\times \text{ 2) + (16 }\times \text{2) + (32 }\times \text{2) = 252 g/mol}$

Interpretation Introduction

Interpretation: To find the mass percent of O in dipyrithione.

Concept Introduction:

  $\text{ Mass \% = }\left(\frac{\text{mass of element}}{\text{molar mass of compound}}\right)\times \text{ 100}$

Answer to Problem 61UTC

Mass percent of O in dipyrithione = 12.7 %

Explanation of Solution

The molecular formula of dipyrithione is C₁₀H₈N₂O₂S₂ Since from the molecular formula of dipyrithione it’s clear that dipyrithione contains 2 atoms of oxygen so, Mass percent of O in dipyrithione = $\left[\frac{\left(\text{16 }\times \text{ 2}\right)}{\text{252}}\right]\times \text{100 = 12}\text{.7\%}$

Interpretation Introduction

Interpretation: To find the grams of C in 2.50 g of dipyrithione.

Concept Introduction: An arithmetical multiplier which is used for converting a quantity expressed in one unit into another equivalent set of units is said to be conversion factor.

Answer to Problem 61UTC

11.9 g of C is present in 2.50 g of dipyrithione.

Explanation of Solution

The molecular formula of dipyrithione is C₁₀H₈N₂O₂S₂ Since from the molecular formula of dipyrithione it’s clear that dipyrithione contains 10 atoms of carbon so,

  $\begin{array}{l}\text{Molar}\text{Mass}\text{of}\text{dipyrithione}\text{Molar}\text{Mass}\text{of}\text{carbon}\\ \text{252}\text{g/mol}\text{10×12}\text{g/mol}\\ \text{25}\text{g}\text{x}\text{g}\end{array}$

Thus,

  $\frac{\text{10×12×25}}{\text{252}}\text{=}\text{11}\text{.9}\text{g}$

Hence, the mass of carbon in 25.0 g of dipyrithione is 11.9 g.

Interpretation Introduction

Interpretation: To find the moles of dipyrithione in 25.0 g of dipyrithione.

Concept Introduction:

The relationship between mass, moles, and molar mass:

  $\text{Moles = }\frac{\text{mass}}{\text{molar mass}}$

Answer to Problem 61UTC

Moles of dipyrithione = 0.0992 mol

Explanation of Solution

The relationship between mass, moles, and molar mass:

  $\text{Moles = }\frac{\text{mass}}{\text{molar mass}}$

Mass of dipyrithione is 25.0 g (given)

Molar mass of dipyrithione is 252 g/mol.

Moles of dipyrithione = $\frac{\text{25}\text{.0 g}}{\text{252 g/mol}}\text{ = 0}\text{.0992 mol}$