Chapter 2, Problem 120GQ

Write the molecular formula and calculate the molar mass for each of the molecules shown here. Which has the largest mass percent of carbon? Of oxygen?

(a) ethylene glycol (used in antifreeze)

(b) dihydroxyacetone (used in artificial tanning lotions)

(c) ascorbic acid, commonly known as vitamin C

Interpretation Introduction

Interpretation: Molar mass and molecular formula of the given compound should be determined and the compound which has the largest mass percent of carbon and oxygen also has to be determined.

Concept Introduction:

• $\text{Mole}\text{of}\text{substance}=\frac{\text{Gram}\text{of}\text{substance}}{\text{Molar}\text{mass}}$
• A chemical formula conveys us the number of atoms of each element in a compound. It contains the symbols of the atoms of the elements present in the compound as well as how many are for each element in the form of subscripts
• The molar mass of an element or compound is the mass in grams of 1 mole of that substance, and it is expressed in the unit of grams per mol (g/mol)
• Mass percentage is one way to represent the concentration of an element in a compound or a component in a mixture. Mass percent of elements of a compound is the ratio of mass of element to the mass of whole compound and multiplied with hundred.

Answer to Problem 120GQ

  $\begin{array}{ccc}\text{Given}\text{Compounds}& \text{Molecular}\text{formula}& \text{Molar}\text{mass}\text{(g/mol)}\\ \text{a)}\text{Ethylene}\text{glycol}& {\text{C}}_{\text{2}}{\text{H}}_{\text{6}}{\text{O}}_{\text{2}}& \text{62}\text{.02}\\ \text{b)}\text{Dihydroacetone}& {\text{C}}_{\text{3}}{\text{H}}_{\text{6}}{\text{O}}_{\text{3}}& \text{90}\text{.03}\\ \text{c)Ascorbic}\text{acid}& {\text{C}}_{\text{6}}{\text{H}}_{\text{8}}{\text{O}}_{\text{6}}& \text{176}\text{.06}\end{array}$

The compound c (ascorbic acid) has high mass percentage of oxygen and high mass percentage of carbon.

Explanation of Solution

Given,

Compound a is,

    

There are two carbon atoms, two oxygen atoms and six hydrogen atoms

Then molecular formula of this compound is $C_2{H}_6{O}_2$

Molar mass of ethylene glycol can be calculated as follows,

$\left(\text{2×}\underset{\text{mass}\text{of}\text{C}}{\text{12}\text{.01}}\right)\text{+}\left(\text{6×}\underset{\text{mass}\text{of}\text{H}}{\text{1}}\right)\text{+}\left(\text{2×}\underset{\text{mass}\text{of}\text{O}}{\text{16}}\right)\text{=}62.02\text{g/mol}$

Given

Compound b is,

    

There are three carbon atoms, three oxygen atoms and six hydrogen atoms

Then molecular formula of this compound is $C_3{H}_6{O}_3$

Molar mass of dihydroxyacetone can be calculated as follows,

$\left(\text{3×}\underset{\text{mass}\text{of}\text{C}}{\text{12}\text{.01}}\right)\text{+}\left(\text{6×}\underset{\text{mass}\text{of}\text{H}}{\text{1}}\right)\text{+}\left(\text{3×}\underset{\text{mass}\text{of}\text{O}}{\text{16}}\right)\text{=}90.03\text{g/mol}$

Similarly,

The given structure of compound c is,

    

There are six carbon atoms, six oxygen atoms and eight hydrogen atoms.

Then molecular formula of this compound is $C_6{H}_8{O}_6$

Molar mass of ascorbic acid can be calculated as follows,

  $\left(\text{6×}\underset{\text{mass}\text{of}\text{C}}{\text{12}\text{.01}}\right)\text{+}\left(\text{8×}\underset{\text{mass}\text{of}\text{H}}{\text{1}}\right)\text{+}\left(\text{6×}\underset{\text{mass}\text{of}\text{O}}{\text{16}}\right)\text{=}176.06\text{g/mol}$

Mass percent of elements of a compound is the ratio of mass of element to the mass of whole compound and multiplied with hundred.

The molecular formula of the given compound a is $C_2{H}_6{O}_2$ and its molar mass is $62.02g/mol$

And this compound namely Ethylene glycol contains two carbon atoms, molar mass of carbon atom is $12.01g/mol$

Molar mass of carbon in compound is $\text{2}\text{×12}\text{.01}\text{=}\text{24}\text{.02}\text{g/mol}$.

$\begin{array}{c}\text{Mass}\text{percent}\text{of}\text{Carbon}\text{in}{C}_2{H}_6{O}_2\text{=}\frac{\text{Molar}\text{mass}\text{of}\text{carbon}}{\text{Molar}\text{mass}\text{of}{C}_2{H}_6{O}_2}\text{×100}\\ \text{=}\frac{24.02}{62.02}\text{×100}\\ \text{=}38.72\text{\%}\end{array}$

Similarly, Molar mass of oxygen in compound $2\text{×16}\text{=}32\text{g/mol}$

$\begin{array}{c}\text{Mass}\text{percent}\text{of}oxygen\text{in}{C}_2{H}_6{O}_2\text{=}\frac{\text{Molar}\text{mass}\text{of}\text{oxygen}}{\text{Molar}\text{mass}\text{of}{C}_2{H}_6{O}_2}\text{×100}\\ \text{=}\frac{32}{62.02}\text{×100}\\ \text{=}51.6\text{\%}\end{array}$

The molecular formula of the given compound b is $C_3{H}_6{O}_3$ and its molar mass is $90.03g/mol$

And this compound namely Dihydroxyacetone contains three carbon atoms, molar mass of carbon atom is $12.01g/mol$

Molar mass of Carbon in compound is $3\text{×12}\text{.01}\text{=}36.03\text{g/mol}$.

$\begin{array}{c}\text{Mass}\text{percent}\text{of}\text{Carbon}\text{in}{C}_3{H}_6{O}_3\text{=}\frac{\text{Molar}\text{mass}\text{of}\text{carbon}}{\text{Molar}\text{mass}\text{of}{C}_3{H}_6{O}_3}\text{×100}\\ \text{=}\frac{36.03}{90.03}\text{×100}\\ \text{=}40.01\text{\%}\end{array}$

Molar mass of oxygen in compound is $3\text{×16}\text{=}48\text{g/mol}$.

$\begin{array}{l}\text{Mass}\text{percent}\text{of}oxygen\text{in}{C}_3{H}_6{O}_3\text{=}\frac{\text{Molar}\text{mass}\text{of}\text{oxygen}}{\text{Molar}\text{mass}\text{of}{C}_3{H}_6{O}_3}\text{×100}\\ \text{=}\frac{48}{90.03}\text{×100}\text{=}53.3\text{\%}\end{array}$

The molecular formula of the given compound c is $C_6{H}_8{O}_6$ and its molar mass is $176.06g/mol$.

And this compound namely ascorbic acid, vitamin C contains six carbon atoms and six oxygen atoms. Molar mass of carbon atom is $12.01g/mol$ and the molar mass of oxygen is $16g/mol$.

Molar mass of carbon in compound is $6\text{×12}\text{.01}\text{=}72.06\text{g/mol}$.

$\begin{array}{c}\text{Mass}\text{percent}\text{of}\text{Carbon}\text{in}{C}_6{H}_8{O}_6\text{=}\frac{\text{Molar}\text{mass}\text{of}\text{carbon}}{\text{Molar}\text{mass}\text{of}{C}_6{H}_8{O}_6}\text{×100}\\ \text{=}\frac{72.06}{176.06}\text{×100}\\ \text{=}40.9\text{\%}\end{array}$

Similarly, Molar mass of oxygen in compound is $6\text{×16}\text{=}96\text{g/mol}$

  $\begin{array}{c}\text{Mass}\text{percent}\text{of}oxygen\text{in}{C}_6{H}_8{O}_6\text{=}\frac{\text{Molar}\text{mass}\text{of}\text{oxygen}}{\text{Molar}\text{mass}\text{of}{C}_3{H}_6{O}_3}\text{×100}\\ \text{=}\frac{96}{176.06}\text{×100}\\ \text{=}54.52\text{\%}\end{array}$

From the above calculations it is clear that the compound c (ascorbic acid) has high mass percentage of oxygen and high mass percentage of carbon.

Conclusion

Molecular formulas, molar mass of the given compound were determined and compound which has high mass percentage of carbon and oxygen in it was identified.