Chapter 6, Problem 6.1EP

Calculate, to two decimal places, the formula mass of each of the following substances. Obtain the needed atomic masses from the inside front cover of the text.

1. a. C₁₂H₂₂O₁₁ (sucrose, table sugar)
2. b. C₇H₁₆ (heptane, a component of gasoline)
3. c. C₇H₅NO₃S (saccharin, an artificial sweetener)
4. d. (NH₄)₂SO₄ (ammonium sulfate, a lawn fertilizer)

Interpretation Introduction

Interpretation:

Formula mass of $C_{12}{H}_{22}{O}_{11}$ has to be calculated.

Concept Introduction:

Sum of atomic masses of all the atoms that are represented in chemical formula of substance is known as formula mass.  If atomic mass and chemical formula of a compound is known, then formula mass can be calculated.

Answer to Problem 6.1EP

Formula mass of sucrose is $342.34amu$.

Explanation of Solution

Given chemical formula is $C_{12}{H}_{22}{O}_{11}$.  The atomic mass of carbon is given as $\text{12}\text{.01}\text{amu}$, for oxygen it is given as $\text{16}\text{.00}\text{amu}$ and for hydrogen it is $1.01amu$.  A formula unit of $C_{12}{H}_{22}{O}_{11}$ contains 45 atoms: twelve carbon atoms, twenty two hydrogen atoms and eleven oxygen atoms.  The formula mass can be calculated as shown below,

$\begin{array}{l}12atomC\text{ X}\left(\frac{\text{12}\text{.01 amu}}{1atomC}\right)\text{=}\text{144}\text{.12}\text{amu}\\ \text{11 atom O X}\left(\frac{\text{16}\text{.00 amu}}{1atomO}\right)\text{=}\text{176}\text{.00}\text{amu}\\ \text{22 atom H X}\left(\frac{\text{1}\text{.01 amu}}{1atomH}\right)\text{=}\text{22}\text{.22}\text{amu}\\ Formulamass=342.34amu\end{array}$

The formula mass of sucrose is calculated as $342.34amu$.

Conclusion

Formula mass of sucrose is calculated.

Interpretation Introduction

Interpretation:

Formula mass of $C_7{H}_{16}$ has to be calculated.

Concept Introduction:

Sum of atomic masses of all the atoms that are represented in chemical formula of substance is known as formula mass.  If atomic mass and chemical formula of a compound is known, then formula mass can be calculated.

Answer to Problem 6.1EP

Formula mass of heptane is $100.23amu$.

Explanation of Solution

Given chemical formula is $C_7{H}_{16}$.  The atomic mass of carbon is given as $\text{12}\text{.01}\text{amu}$ and for hydrogen it is $1.01amu$.  A formula unit of $C_7{H}_{16}$ contains 23 atoms: seven carbon atoms and sixteen hydrogen atoms.  The formula mass can be calculated as shown below,

$\begin{array}{l}7atomC\text{ X}\left(\frac{\text{12}\text{.01 amu}}{1atomC}\right)\text{=}\text{84}\text{.07}\text{amu}\\ \text{16 atom H X}\left(\frac{\text{1}\text{.01 amu}}{1atomH}\right)\text{=}\text{16}\text{.16}\text{amu}\\ Formulamass=100.23amu\end{array}$

The formula mass of heptane is calculated as $100.23amu$.

Conclusion

Formula mass of heptane is calculated.

Interpretation Introduction

Interpretation:

Formula mass of $C_7{H}_{5}N{O}_{3}S$ has to be calculated.

Concept Introduction:

Sum of atomic masses of all the atoms that are represented in chemical formula of substance is known as formula mass.  If atomic mass and chemical formula of a compound is known, then formula mass can be calculated.

Answer to Problem 6.1EP

Formula mass of saccharin is $183.20amu$.

Explanation of Solution

Given chemical formula is $C_7{H}_{5}N{O}_{3}S$.  The atomic mass of carbon is given as $\text{12}\text{.01}\text{amu}$, for oxygen it is given as $\text{16}\text{.00}\text{amu}$, for nitrogen it is $14.01amu$, for sulfur it is $32.07amu$ and for hydrogen it is $1.01amu$.  A formula unit of $C_7{H}_{5}N{O}_{3}S$ contains 17 atoms: seven carbon atoms, five hydrogen atoms, one nitrogen atom, three oxygen atoms and one sulfur atom.  The formula mass can be calculated as shown below,

$\begin{array}{l}7atomC\text{ X}\left(\frac{\text{12}\text{.01 amu}}{1atomC}\right)\text{=}\text{84}\text{.07}\text{amu}\\ \text{3 atom O X}\left(\frac{\text{16}\text{.00 amu}}{1atomO}\right)\text{=}\text{48}\text{.00}\text{amu}\\ \text{5 atom H X}\left(\frac{\text{1}\text{.01 amu}}{1atomH}\right)\text{=}\text{5}\text{.05}\text{amu}\\ \text{1 atom N X}\left(\frac{\text{14}\text{.01 amu}}{1atomN}\right)\text{=}\text{14}\text{.01}\text{amu}\\ \text{1 atom S X}\left(\frac{\text{32}\text{.07 amu}}{1atomS}\right)\text{=}\text{32}\text{.07}\text{amu}\\ Formulamass=183.20amu\end{array}$

The formula mass of saccharin is calculated as $183.20amu$.

Conclusion

Formula mass of saccharin is calculated.

Interpretation Introduction

Interpretation:

Formula mass of ${(N{H}_4)}_{2}S{O}_4$ has to be calculated.

Concept Introduction:

Sum of atomic masses of all the atoms that are represented in chemical formula of substance is known as formula mass.  If atomic mass and chemical formula of a compound is known, then formula mass can be calculated.

Answer to Problem 6.1EP

Formula mass of ammonium sulfate is $132.17amu$.

Explanation of Solution

Given chemical formula is ${(N{H}_4)}_{2}S{O}_4$.  The atomic mass of oxygen is given as $\text{16}\text{.00}\text{amu}$, for nitrogen it is $14.01amu$, for sulfur it is $32.07amu$ and for hydrogen it is $1.01amu$.  A formula unit of ${(N{H}_4)}_{2}S{O}_4$ contains 15 atoms: eight hydrogen atoms, two nitrogen atoms, four oxygen atoms and one sulfur atom.  The formula mass can be calculated as shown below,

$\begin{array}{l}\text{4 atom O X}\left(\frac{\text{16}\text{.00 amu}}{1atomO}\right)\text{=}\text{64}\text{.00}\text{amu}\\ \text{8 atom H X}\left(\frac{\text{1}\text{.01 amu}}{1atomH}\right)\text{=}\text{8}\text{.08}\text{amu}\\ \text{2 atom N X}\left(\frac{\text{14}\text{.01 amu}}{1atomN}\right)\text{=}\text{28}\text{.02}\text{amu}\\ \text{1 atom S X}\left(\frac{\text{32}\text{.07 amu}}{1atomS}\right)\text{=}\text{32}\text{.07}\text{amu}\\ Formulamass=132.17amu\end{array}$

The formula mass of ammonium sulfate is calculated as $132.17amu$.

Conclusion

Formula mass of ammonium sulfate is calculated.