Chapter 3, Problem 3.34QP

(a)

Interpretation Introduction

Interpretation: Molar mass of the given sweetener molecules are to be calculated.

Concept introduction: Molar mass is a physical quantity to measure the mass of the atoms. The mass in grams of one mole of any substance is known as the molar mass of that substance. It is represented by the symbol $M$. In case of molecules the molar mass of the molecule is the sum of molar mass of all the atoms present in that molecule. Generally the molar mass of the compound is expressed in $\text{g/mol}$.

To determine: The molar mass of the sweetener molecule sucrose ${\text{C}}_{12}{\text{H}}_{12}{\text{O}}_{11}$.

Answer to Problem 3.34QP

Solution

The molar mass of the ${\text{C}}_{12}{\text{H}}_{12}{\text{O}}_{11}$ molecule is $\underset{\_}{332.2202g/mol}$.

Explanation of Solution

Explanation

The given ${\text{C}}_{12}{\text{H}}_{12}{\text{O}}_{11}$ molecule consists of one manganese atom, one silicon atom and three oxygen atoms.

Therefore, the molar mass of the given molecule is the sum of all the atoms present in the molecule.

The molar mass of the carbon, hydrogen and oxygen atoms are $12.0107\text{g/mol,}\text{1}\text{.0079}\text{g/mol}\text{and}15.9994\text{g/mol}$ respectively. Hence, the molar mass of the ${\text{C}}_{12}{\text{H}}_{12}{\text{O}}_{11}$ molecule is calculated by the given formula,

$M_{{\text{C}}_{12}{\text{H}}_{12}{\text{O}}_{11}}=12M_{\text{C}}+12M_{\text{H}}+11M_{\text{O}}$

Where,

• $M_{{\text{C}}_{12}{\text{H}}_{12}{\text{O}}_{11}}$ represents the molar mass of the ${\text{C}}_{12}{\text{H}}_{12}{\text{O}}_{11}$ molecule.
• $M_{\text{C}}$ represents the atomic mass of the $\text{C}$ atom.
• $M_{\text{H}}$ represents the atomic mass of the $\text{H}$ atom.
• $M_{\text{O}}$ represents the atomic mass of the $\text{O}$ atom.

Substitute the values in the above formula.

$\begin{array}{c}{M}_{{\text{C}}_{12}{\text{H}}_{12}{\text{O}}_{11}}=12M_{\text{C}}+12M_{\text{H}}+11M_{\text{O}}\\ M_{{\text{C}}_{12}{\text{H}}_{12}{\text{O}}_{11}}=12\left(12.0107\text{g/mol}\right)+12\left(1.0079\text{g/mol}\right)+11\left(15.9994\text{g/mol}\right)\\ M_{{\text{C}}_{12}{\text{H}}_{12}{\text{O}}_{11}}=\left(144.1284\text{g/mol}\right)+\left(12.0948\text{g/mol}\right)+\left(175.9934\text{g/mol}\right)\\ M_{{\text{C}}_{12}{\text{H}}_{12}{\text{O}}_{11}}=\underset{\_}{332.2202g/mol}\end{array}$

(b)

Interpretation Introduction

To determine: The molar mass of the sweetener molecule saccharin ${\text{C}}_7{\text{H}}_5{\text{NO}}_3\text{S}$.

Answer to Problem 3.34QP

Solution

The molar mass of the ${\text{C}}_7{\text{H}}_5{\text{NO}}_3\text{S}$ molecule is $\underset{\_}{164.2006g/mol}$.

Explanation of Solution

Explanation

The given ${\text{C}}_7{\text{H}}_5{\text{NO}}_3\text{S}$ molecule consists of one calcium atom, one tungsten atom and four oxygen atoms.

Therefore, the molar mass of the given molecule is the sum of all the atoms present in the molecule.

Hence, the molar mass of the ${\text{C}}_7{\text{H}}_5{\text{NO}}_3\text{S}$ molecule is calculated by the given formula,

$M_{{\text{C}}_7{\text{H}}_5{\text{NO}}_3\text{S}}=7M_{\text{C}}+5M_{\text{H}}+M_{\text{N}}+3M_{\text{O}}+M_{\text{S}}$

Where,

• $M_{{\text{C}}_7{\text{H}}_5{\text{NO}}_3\text{S}}$ represents the molar mass of the ${\text{C}}_7{\text{H}}_5{\text{NO}}_3\text{S}$ molecule.
• $M_{\text{N}}$ represents the atomic mass of the $\text{N}$ atom.
• $M_{\text{S}}$ represents the atomic mass of the $\text{S}$ atom.

Substitute the values in the above formula.

$\begin{array}{c}{M}_{{\text{C}}_7{\text{H}}_5{\text{NO}}_3\text{S}}=7M_{\text{C}}+5M_{\text{H}}+M_{\text{N}}+3M_{\text{O}}+M_{\text{S}}\\ M_{{\text{C}}_7{\text{H}}_5{\text{NO}}_3\text{S}}=\left[\begin{array}{l}7\left(12.0107\text{g/mol}\right)+5\left(1.0079\text{g/mol}\right)+\\ \left(14.0067\text{g/mol}\right)+3\left(15.9994\text{g/mol}\right)+\\ \left(32.0650\text{g/mol}\right)\end{array}\right]\\ M_{{\text{C}}_7{\text{H}}_5{\text{NO}}_3\text{S}}=\underset{\_}{183.1800g/mol}\end{array}$

(c)

Interpretation Introduction

To determine: The molar mass of the sweetener molecule aspartame ${\text{C}}_{14}{\text{H}}_{18}{\text{N}}_2{\text{O}}_5$.

Answer to Problem 3.34QP

Solution

The molar mass of the ${\text{C}}_{14}{\text{H}}_{18}{\text{N}}_2{\text{O}}_5$ molecule is $\underset{\_}{294.3012g/mol}$.

Explanation of Solution

Explanation

The given ${\text{C}}_{14}{\text{H}}_{18}{\text{N}}_2{\text{O}}_5$ molecule consists of one iron, one titanium and three oxygen atoms.

Therefore, the molar mass of the given molecule is the sum of all the atoms present in the molecule.

Hence, the molar mass of the ${\text{C}}_{14}{\text{H}}_{18}{\text{N}}_2{\text{O}}_5$ molecule is calculated by the given formula,

$M_{{\text{C}}_{14}{\text{H}}_{18}{\text{N}}_2{\text{O}}_5}=14M_{\text{C}}+18M_{\text{H}}+2M_{\text{N}}+5M_{\text{O}}$

Where,

• $M_{{\text{C}}_{14}{\text{H}}_{18}{\text{N}}_2{\text{O}}_5}$ represents the molar mass of the ${\text{C}}_{14}{\text{H}}_{18}{\text{N}}_2{\text{O}}_5$ molecule.

Substitute the values in the above formula.

$\begin{array}{c}{M}_{{\text{C}}_{14}{\text{H}}_{18}{\text{N}}_2{\text{O}}_5}=14M_{\text{C}}+18M_{\text{H}}+2M_{\text{N}}+5M_{\text{O}}\\ M_{{\text{C}}_{14}{\text{H}}_{18}{\text{N}}_2{\text{O}}_5}=\left(\begin{array}{l}14\left(12.0107\text{g/mol}\right)+18\left(1.0079\text{g/mol}\right)\\ +2\left(15.0100\text{g/mol}\right)+5\left(15.9994\text{g/mol}\right)\end{array}\right)\\ M_{{\text{C}}_{14}{\text{H}}_{18}{\text{N}}_2{\text{O}}_5}=\underset{\_}{294.3012g/mol}\end{array}$

(d)

Interpretation Introduction

To determine: The molar mass of the sweetener molecule fructose ${\text{C}}_6{\text{H}}_{12}{\text{O}}_6$.

Answer to Problem 3.34QP

Solution

The molar mass of the ${\text{C}}_6{\text{H}}_{12}{\text{O}}_6$ molecule is $\underset{\_}{180.1607g/mol}$.

Explanation of Solution

Explanation

The given ${\text{C}}_6{\text{H}}_{12}{\text{O}}_6$ molecule consists of one magnesium atom, one carbon atom and three oxygen atoms.

Therefore, the molar mass of the given molecule is the sum of all the atoms present in the molecule.

Hence, the molar mass of the ${\text{C}}_6{\text{H}}_{12}{\text{O}}_6$ molecule is calculated by the given formula,

$M_{{\text{C}}_6{\text{H}}_{12}{\text{O}}_6}=6M_{\text{C}}+12M_{\text{H}}+6M_{\text{O}}$

Where,

• $M_{{\text{C}}_6{\text{H}}_{12}{\text{O}}_6}$ represents the molar mass of the ${\text{C}}_6{\text{H}}_{12}{\text{O}}_6$ molecule.

Substitute the values in the above formula.

$\begin{array}{c}{M}_{{\text{C}}_6{\text{H}}_{12}{\text{O}}_6}=6M_{\text{C}}+12M_{\text{H}}+6M_{\text{O}}\\ M_{{\text{C}}_6{\text{H}}_{12}{\text{O}}_6}=6\left(12.0107\text{g/mol}\right)+12\left(1.0079\text{g/mol}\right)+6\left(15.9994\text{g/mol}\right)\\ M_{{\text{C}}_6{\text{H}}_{12}{\text{O}}_6}=\underset{\_}{180.1607g/mol}\end{array}$

Conclusion

1. a) The molar mass of the ${\text{C}}_{12}{\text{H}}_{12}{\text{O}}_{11}$ is $\underset{\_}{332.2202g/mol}$.
2. b) The molar mass of the ${\text{C}}_7{\text{H}}_5{\text{NO}}_3\text{S}$ is $\underset{\_}{183.1800g/mol}$.
3. c) The molar mass of the ${\text{C}}_{14}{\text{H}}_{18}{\text{N}}_2{\text{O}}_5$ is $\underset{\_}{294.3012g/mol}$.
4. d) The molar mass of the ${\text{C}}_6{\text{H}}_{12}{\text{O}}_6$ is $\underset{\_}{180.1607g/mol}$