Chapter 8, Problem 49QAP

Interpretation Introduction

(a)

Interpretation:

The percent by mass of element listed first in the formula of a compound should be calculated.

Concept Introduction:

A chemical compound is a collection of several atoms. Molar masses of each and every atom collectively provide the molar mass of that compound.

$\text{mass fraction for a given element =}\frac{\text{mass of the element present in 1 mole of compound}}{\text{mass of 1 mole of compound}}$

Mass fraction for a given element can be converted into mass percent by multiplying $100\text{\%}.$.

Answer to Problem 49QAP

$49.31\text{\%}$.

Explanation of Solution

The compound is adipic acid, ${\text{C}}_{\text{6}}{\text{H}}_{\text{10}}{\text{O}}_{\text{4}}$. Here, the first atom is Carbon.

Molar mass of carbon is 12.01 g/mol, hydrogen is 1.008 g/mol and oxygen is 16.0 g/mol.

Thus, the molar mass of adipic acid can be calculated as follows:

$\begin{array}{c}\text{M}=6\times 12.01\text{ g/mol+10}\times \text{1}\text{.008 g/mol+4}\times \text{16}\text{.0 g/mol}\\ \text{=146}\text{.14 g/mol}\end{array}$

Now, mass of carbon in 1 mol is 12.01 g thus, mass of 6 mol of carbon will be:

${\text{M}}_{\text{C}}=6\times 12.01\text{ g}=72.06\text{ g}$

Mass of adipic acid in 1 mol is 146.14 g.

Thus, mass percent of C can be calculated as follows:

$\begin{array}{c}\text{\%}\text{M}=\frac{72.06\text{ g C}}{146.14{\text{ g C}}_{\text{6}}{\text{H}}_{\text{10}}{\text{O}}_{\text{4}}}\times 100\text{\%}\\ =49.31\text{\%}\end{array}$.

Interpretation Introduction

(b)

Interpretation:

The percent by mass of element listed first in the formula of a compound should be calculated.

Concept Introduction:

A chemical compound is a collection of several atoms. Molar masses of each and every atom collectively provide the molar mass of that compound.

$\text{mass fraction for a given element =}\frac{\text{mass of the element present in 1 mole of compound}}{\text{mass of 1 mole of compound}}$

Mass fraction for a given element can be converted into mass percent by multiplying $100\text{\%}.$.

Answer to Problem 49QAP

$35\text{\%}$.

Explanation of Solution

The compound is ammonium nitrate ${\text{NH}}_{\text{4}}{\text{NO}}_{\text{3}}$. Here, the first atom is nitrogen.

Molar mass of nitrogen is 14 g/mol, hydrogen is 1.008 g/mol and oxygen is 16.0 g/mol.

Thus, the molar mass of ammonium nitrate can be calculated as follows:

$\begin{array}{c}\text{M}=2\times 14\text{ g/mol+4}\times \text{1}\text{.008 g/mol+3}\times \text{16}\text{.0 g/mol}\\ \text{=80}\text{.043 g/mol}\end{array}$

Now, mass of nitrogen in 1 mol is 14 g thus, mass of nitrogen in 2 mol is 28 g.

Mass of ammonium nitrate in 1 mol is 80.043 g.

Thus, mass percent of N can be calculated as follows:

$\begin{array}{c}\text{\%}\text{M}=\frac{\text{28 g N}}{80.043{\text{ g NH}}_{\text{4}}{\text{NO}}_{\text{3}}}\times 100\text{\%}\\ =35\text{\%}\end{array}$.

Interpretation Introduction

(c)

Interpretation:

The percent by mass of element listed first in the formula of a compound should be calculated.

Concept Introduction:

A chemical compound is a collection of several atoms. Molar masses of each and every atom collectively provide the molar mass of that compound.

$\text{mass fraction for a given element =}\frac{\text{mass of the element present in 1 mole of compound}}{\text{mass of 1 mole of compound}}$

Mass fraction for a given element can be converted into mass percent by multiplying $100\text{\%}.$.

Answer to Problem 49QAP

$49.5\text{\%}$.

Explanation of Solution

The compound is caffeine ${\text{C}}_{\text{8}}{\text{H}}_{\text{10}}{\text{N}}_{\text{4}}{\text{O}}_{\text{2}}$. Here, the first atom is carbon.

Molar mass of carbon is 12.01 g/mol, hydrogen is 1.008 g/mol, nitrogen is 14 g/mol and oxygen is 16.0 g/mol.

Thus, the molar mass of caffeine can be calculated as follows:

$\begin{array}{c}\text{M}=8\times 12.01\text{ g/mol}+4\times 14\text{ g/mol+10}\times \text{1}\text{.008 g/mol+2}\times \text{16}\text{.0 g/mol}\\ \text{=194}\text{.2 g/mol}\end{array}$

Now, mass of carbon in 1 mol is 12.01 g thus, mass of carbon in 8 mol will be:

${\text{M}}_{\text{C}}=8\times 12.01\text{ g}=96.08\text{ g}$

Mass of caffeine in 1 mol is 194.2 g.

Thus, mass percent of C can be calculated as follows:

$\begin{array}{c}\text{\%}\text{M}=\frac{\text{96}\text{.08 g C}}{194.2{\text{ g C}}_{\text{8}}{\text{H}}_{\text{10}}{\text{N}}_{\text{4}}{\text{O}}_{\text{2}}}\times 100\text{\%}\\ =49.5\text{\%}\end{array}$.

Interpretation Introduction

(d)

Interpretation:

The percent by mass of element listed first in the formula of a compound should be calculated.

Concept Introduction:

A chemical compound is a collection of several atoms. Molar masses of each and every atom collectively provide the molar mass of that compound.

$\text{mass fraction for a given element =}\frac{\text{mass of the element present in 1 mole of compound}}{\text{mass of 1 mole of compound}}$

Mass fraction for a given element can be converted into mass percent by multiplying $100\text{\%}.$.

Answer to Problem 49QAP

$52.45\text{\%}$.

Explanation of Solution

The compound is chlorine dioxide ${\text{ClO}}_{\text{2}}$. Here, the first atom is chlorine.

Molar mass of chlorine is 35.5 g/mol and oxygen is 16.0 g/mol.

Thus, the molar mass of chlorine dioxide can be calculated as follows:

$\begin{array}{c}\text{M}=1\times 35.5\text{ g/mol+2}\times \text{16}\text{.0 g/mol}\\ \text{=67}\text{.5 g/mol}\end{array}$

Now, mass of chlorine in 1 mol is 35.5 g and mass of chlorine dioxide in 1 mol is 67.5 g.

Thus, mass percent of Cl can be calculated as follows:

$\begin{array}{c}\text{\%}\text{M}=\frac{\text{35}\text{.5 g Cl}}{67.5{\text{ g ClO}}_{\text{2}}}\times 100\text{\%}\\ =52.45\text{\%}\end{array}$.

Interpretation Introduction

(e)

Interpretation:

The percent by mass of element listed first in the formula of a compound should be calculated.

Concept Introduction:

A chemical compound is a collection of several atoms. Molar masses of each and every atom collectively provide the molar mass of that compound.

$\text{mass fraction for a given element =}\frac{\text{mass of the element present in 1 mole of compound}}{\text{mass of 1 mole of compound}}$

Mass fraction for a given element can be converted into mass percent by multiplying $100\text{\%}.$.

Answer to Problem 49QAP

$72\text{\%}$.

Explanation of Solution

The compound is cyclohexanol ${\text{C}}_{\text{6}}{\text{H}}_{\text{11}}\text{OH}$. Here, the first atom is carbon.

Molar mass of carbon is 12.01 g/mol, molar mass of hydrogen is 1.008 g/mol and oxygen is 16.0 g/mol.

Thus, the molar mass of cyclohexanol can be calculated as follows:

$\begin{array}{c}\text{M}=6\times 12.01\text{ g/mol+}12\times 1.008\text{ g/mol+1}\times \text{16}\text{.0 g/mol}\\ \text{=100}\text{.16 g/mol}\end{array}$

Now, mass of carbon in 1 mol is 12.01 g thus, mass of carbon in 6 mol is 72.06 g.

Mass of cyclohexanol in 1 mol is 100.16 g.

Thus, mass percent of C can be calculated as follows:

$\begin{array}{c}\text{\%}\text{M}=\frac{\text{72}\text{.06 g C}}{100.16{\text{ g C}}_{\text{6}}{\text{H}}_{\text{11}}\text{OH}}\times 100\text{\%}\\ =72\text{\%}\end{array}$.

Interpretation Introduction

(f)

Interpretation:

The percent by mass of element listed first in the formula of a compound should be calculated.

Concept Introduction:

A chemical compound is a collection of several atoms. Molar masses of each and every atom collectively provide the molar mass of that compound.

$\text{mass fraction for a given element =}\frac{\text{mass of the element present in 1 mole of compound}}{\text{mass of 1 mole of compound}}$

Mass fraction for a given element can be converted into mass percent by multiplying $100\text{\%}.$.

Answer to Problem 49QAP

$40\text{\%}$.

Explanation of Solution

The compound is dextrose ${\text{C}}_{\text{6}}{\text{H}}_{\text{12}}{\text{O}}_6$. Here, the first atom is carbon.

Molar mass of carbon is 12.01 g/mol, molar mass of hydrogen is 1.008 g/mol and oxygen is 16.0 g/mol.

Thus, the molar mass of dextrose can be calculated as follows:

$\begin{array}{c}\text{M}=6\times 12.01\text{ g/mol+}12\times 1.008\text{ g/mol+6}\times \text{16}\text{.0 g/mol}\\ \text{=180}\text{.16 g/mol}\end{array}$

Now, mass of carbon in 1 mol is 12.01 g thus, mass of carbon in 6 mol is 72.06 g.

Mass of cyclohexanol in 1 mol is 100.16 g.

Thus, mass percent of C can be calculated as follows:

$\begin{array}{c}\text{\%}\text{M}=\frac{\text{72}\text{.06 g C}}{180.16{\text{ g C}}_{\text{6}}{\text{H}}_{\text{11}}\text{OH}}\times 100\text{\%}\\ =40\text{\%}\end{array}$.

Interpretation Introduction

(g)

Interpretation:

The percent by mass of element listed first in the formula of a compound should be calculated.

Concept Introduction:

A chemical compound is a collection of several atoms. Molar masses of each and every atom collectively provide the molar mass of that compound.

$\text{mass fraction for a given element =}\frac{\text{mass of the element present in 1 mole of compound}}{\text{mass of 1 mole of compound}}$

Mass fraction for a given element can be converted into mass percent by multiplying $100\text{\%}.$.

Answer to Problem 49QAP

$85\text{\%}$.

Explanation of Solution

The compound is eicosane ${\text{C}}_{20}{\text{H}}_{\text{42}}$. Here, the first atom is carbon.

Molar mass of carbon is 12.01 g/mol and molar mass of hydrogen is 1.008 g/mol.

Thus, the molar mass of eicosane can be calculated as follows:

$\begin{array}{c}\text{M}=20\times 12.01\text{ g/mol+}42\times 1.008\text{ g/mol}\\ \text{=282}\text{.55 g/mol}\end{array}$

Now, mass of carbon in 1 mol is 12.01 g thus, mass of carbon in 20 mol is 240.2 g.

Mass of eicosane in 1 mol is 282.55 g.

Thus, mass percent of C can be calculated as follows:

$\begin{array}{c}\text{\%}\text{M}=\frac{\text{240}\text{.2 g C}}{282.55{\text{ g C}}_{20}{\text{H}}_{\text{42}}}\times 100\text{\%}\\ =85\text{\%}\end{array}$.

Interpretation Introduction

(h)

Interpretation:

The percent by mass of element listed first in the formula of a compound should be calculated.

Concept Introduction:

A chemical compound is a collection of several atoms. Molar masses of each and every atom collectively provide the molar mass of that compound.

$\text{mass fraction for a given element =}\frac{\text{mass of the element present in 1 mole of compound}}{\text{mass of 1 mole of compound}}$

Mass fraction for a given element can be converted into mass percent by multiplying $100\text{\%}.$.

Answer to Problem 49QAP

$52.01\text{\%}$.

Explanation of Solution

The compound is ethanol ${\text{C}}_{\text{2}}{\text{H}}_{\text{5}}\text{OH}$. Here, the first atom is carbon.

Molar mass of carbon is 12.01 g/mol molar mass of oxygen is 16.0 g/mol and molar mass of hydrogen is 1.008 g/mol.

Thus, the molar mass of ethanol can be calculated as follows:

$\begin{array}{c}\text{M}=2\times 12.01\text{ g/mol+6}\times 1.008\text{ g/mol+1}\times \text{16 g/mol}\\ \text{=46}\text{.1 g/mol}\end{array}$

Now, mass of carbon in 1 mol is 12.01 g thus, mass of carbon in 2 mol is 24.02 g.

Mass of ethanol in 1 mol is 46.1 g.

Thus, mass percent of C can be calculated as follows:

$\begin{array}{c}\text{\%}\text{M}=\frac{\text{24}\text{.02 g C}}{\text{46}{\text{.1 g C}}_{\text{2}}{\text{H}}_{\text{5}}\text{OH}}\times 100\text{\%}\\ =52.10\text{\%}\end{array}$.