Question

You take $\mathbf{1}\mathbf{.00}$g of an aspirin (a compound consisting solely of carbon, hydrogen, and oxygen), burn it in air, and collect $\mathbf{2}\mathbf{.20}{\mathbf{\text{\hspace{0.17em}g\hspace{0.17em}CO}}}_{\mathbf{\text{2}}}$and $\mathbf{0}\mathbf{.400}{\mathbf{\text{\hspace{0.17em}g\hspace{0.17em}H}}}_{\mathbf{\text{2}}}\mathbf{\text{O}}$.You know that the molar mass of aspirin is between$\mathbf{170}$and$\mathbf{190}\raisebox{1ex}{$\mathbf{\text{g}}$}\!\left/ \!\raisebox{-1ex}{$\mathbf{\text{mol}}$}\right.$. Reacting 1 mole of salicylic acid with 1 mole of acetic anhydride${\mathbf{\text{(C}}}_{\mathbf{\text{4}}}{\mathbf{\text{H}}}_{\mathbf{\text{6}}}{\mathbf{\text{O}}}_{\mathbf{\text{3}}}\mathbf{\text{)}}$gives you 1 mole of aspirin and mole of acetic acid.${\mathbf{\text{(C}}}_{\mathbf{\text{2}}}{\mathbf{\text{H}}}_{\mathbf{\text{4}}}{\mathbf{\text{O}}}_{\mathbf{\text{2}}}\mathbf{\text{)}}$Use this information to determine the molecular formula of salicylic acid

Short answer

Molecular formula of aspirine is$C_9{H}_8{O}_4$

Molecular formula of salicylic acid is$C_7{H}_6{O}_3$

Step-by-step solution

Definition of molecular formula

A chemical formula that gives the total number of atoms of each element in each molecule of a substance is defined as molecular formula

Calculation for molecular formula of aspirine

$C_x{H}_y{O}_z\to C{O}_2+H_{2}O$

$\begin{array}{c}n\left(C{O}_2\right)=\frac{m}{Mr}\\ =\frac{2.20g}{\raisebox{1ex}{$44g$}\!\left/ \!\raisebox{-1ex}{$\text{mole}$}\right.}\\ n\left(C{O}_2\right)=0.05\text{mole}\end{array}$

$\begin{array}{c}\frac{n\left(C{O}_2\right)}{n\left(H_{2}0\right)}=\frac{0.05\text{mole}}{0.022\text{mole}}\\ =\frac{9}{4}\end{array}$

In this chemical reaction, there are 9 moles of $C{O}_2$and moles of$H_{2}O$

Calculation of moles of aspirin

$\begin{array}{c}\text{Molar\hspace{0.17em}ratio}=\frac{n\left(C{O}_2\right)}{n\left(\text{aspirine}\right)}\\ =\frac{9}{1}\to n\left(\text{aspirine}\right)\\ =\frac{1}{9}\times 0.05\text{mole}\\ \text{Molar\hspace{0.17em}ratio}=5.56\times {10}^{-3}\text{mole}\end{array}$

$\begin{array}{l}\text{Mr(aspirine)}=\frac{1g}{5.56\times {10}^{-3}}\\ =\frac{180g}{\text{mole}}\\ \raisebox{1ex}{$9.12g$}\!\left/ \!\raisebox{-1ex}{$\text{mole}$}\right.+\raisebox{1ex}{$8.1g$}\!\left/ \!\raisebox{-1ex}{$\text{mole}$}\right.+x.\raisebox{1ex}{$16g$}\!\left/ \!\raisebox{-1ex}{$\text{mole}$}\right.\to x=4\end{array}$

The molecular formula of aspirine is$C_9{H}_8{O}_4$

Calculation for molecular formula of salicylic acid

$C_x{H}_y{O}_z+C_4{H}_6{O}_3\to C_9{H}_8{O}_4+C_2{H}_4{O}_2$

All molecules are present with mole; it is easy to calculate the number of atoms by sum up all the atoms on right and left side

$\begin{array}{l}XC+4C=9C+2C\to X=7\\ YH+6H=8H+4H\to Y=6\\ ZO+3O04O+2O\to Z=3\end{array}$

The molecular formula of salicylic acid is$C_7{H}_6{O}_3$