Q. 7.17 - An Introduction to General, Organic, and Biological Chemistry

Question

Calculate the molar mass for each of the following:

a. ${\mathrm{Al}}_2{\left({\mathrm{SO}}_4\right)}_3$ , antiperspirant

b. ${\mathrm{KC}}_4{\mathrm{H}}_5{\mathrm{O}}_6$, cream of tartar

C. ${\mathrm{C}}_{16}{\mathrm{H}}_{19}{\mathrm{N}}_3{\mathrm{O}}_5\mathrm{S}$, amoxicillin, antibiotic

Step-by-Step Solution

Answer

a. The molar mass of ${\mathrm{Al}}_2{\left({\mathrm{SO}}_4\right)}_3$ is $342.02 \mathrm{g}$

b. The molar mass of ${\mathrm{KC}}_4{\mathrm{H}}_5{\mathrm{O}}_6$ is $187.07 \mathrm{g}$

c. The molar mass of ${\mathrm{C}}_{16}{\mathrm{H}}_{19}{\mathrm{N}}_3{\mathrm{O}}_5\mathrm{S}$ is $365.17 \mathrm{g}$

Part (a) Step 1 : Given information

We have to find the molar mass of ${\mathrm{Al}}_2{\left({\mathrm{SO}}_4\right)}_3$

Part (a) Step 2 : Simplification

We know that,

Molar mass of one $\mathrm{Al}$ atom = $26.98 \mathrm{g}$

Molar mass of one $\mathrm{S}$ atom = $32.06 \mathrm{g}$

Molar mass of one $\mathrm{O}$ atom = $15.99 \mathrm{g}$

So, the molar mass of ${\mathrm{Al}}_2{\left({\mathrm{SO}}_4\right)}_3$ = $2\left(26.98\right) + 3\left(32.06\right)\hspace{0.17em}+ 12\left(15.99\right)$ = $342.02 \mathrm{g}$

Part (b) Step 1 : Given information

We have to find the molar mass of ${\mathrm{KC}}_4{\mathrm{H}}_5{\mathrm{O}}_6$

Part (b) Step 2 : Simplification

We know that,

Molar mass of one $\mathrm{K}$ atom = $38.09 \mathrm{g}$

Molar mass of one $\mathrm{C}$ atom = $12.01 \mathrm{g}$

Molar mass of one $\mathrm{H}$ atom = $1.00 \mathrm{g}$

Molar mass of one $\mathrm{O}$ atom = $15.99 \mathrm{g}$

So, the molar mass of ${\mathrm{KC}}_4{\mathrm{H}}_5{\mathrm{O}}_6$ = $38.09 + 4\left(12.01\right) + 5\left(1.00\right) + 6\left(15.99\right)$ = $187.07 \mathrm{g}$

Part (c) Step 1 : Given information

We have to find the molar mass of ${\mathrm{C}}_{16}{\mathrm{H}}_{19}{\mathrm{N}}_3{\mathrm{O}}_5\mathrm{S}$

Part (c) Step 2 : Simplification

We know that,

Molar mass of one $\mathrm{C}$ atom = $12.01 \mathrm{g}$

Molar mass of one $\mathrm{H}$  atom = $1.00 \mathrm{g}$

Molar mass of one $\mathrm{N}$ atom = $14.00 \mathrm{g}$

Molar mass of one $\mathrm{O}$ atom = $15.99 \mathrm{g}$

Molar mass of one $\mathrm{S}$ atom = $32.06 \mathrm{g}$

So, the molar mass of ${\mathrm{C}}_{16}{\mathrm{H}}_{19}{\mathrm{N}}_3{\mathrm{O}}_5\mathrm{S}$ = $16\left(12.01\right) + 19\left(1.00\right) + 3\left(14.00\right) + 5\left(15.99\right) + 32.06$

                                                                 = $365.17 \mathrm{g}$