Chapter 3, Problem 146AP

Aspirin or acetylsalicylic acid is synthesized by combining salicylic acid with acetic anhydride:

$\begin{array}{l}{\text{C}}_{\text{2}}{\text{H}}_{\text{6}}{\text{O}}_{\text{3}}{\text{+ C}}_{\text{4}}{\text{H}}_{\text{6}}{\text{O}}_{\text{3}}\underset{}{\to }{\text{ C}}_{\text{9}}{\text{H}}_{\text{8}}{\text{O}}_{\text{4}}{\text{+ HC}}_{\text{2}}{\text{H}}_{\text{3}}{\text{O}}_{\text{2}}\\ \text{salicylic acid acetic dride aspirin acetic acid}\end{array}$

(a) How much salicylic acid is required to produce 0.400 g of aspirin (about the content in a tablet), assuming acetic anhydride is present in excess? (b) Calculate the amount of salicylic acid needed if only 74.9 percent of salicylic is converted to aspirin. (c) In one experiment. 9.26 g of salicylic acid reacts with 8.54 g of acetic anhydride. Calculate the theoretical yield of aspirin and the percent yield if only 10.9 g of aspirin is produced.

Interpretation Introduction

Interpretation:

The amount of salicylic acid at the given conditions, the theoretical yield, and the percent yield of aspirin in the reaction are to be calculated.

Concept introduction:

Atomic mass of elements is measured in terms of atomic mass unit. One atomic mass unit is defined as the number of elementary particles present in $12.0\text{g}$ of carbon atoms.

The number of moles are given by the following expression:

$n=\frac{\text{given mass}\left(m\right)}{\text{molar mass}\left(M\right)}$

The percent yield of the compound is given by the following expression:

$\text{Percent}\text{yield}=\frac{\text{observed yield}}{\text{actual yield}}\times 100$

The mass of compound can be calculated as $m=n\times M$.

Here, $n$ is the number of moles, $m$ is the mass, and $M$ is the molar mass.

The mass of salicylic acid is given by the expression:

$n_{\text{aspirin}}\times \left(M_{\text{salicylic acid}}\right)=\left(m_{\text{salicylic acid}}\right)$

$\frac{m_{\text{aspirin}}}{M_{\text{aspirin}}}\times \left(M_{\text{salicylic acid}}\right)=\left(m_{\text{salicylic acid}}\right)$

Answer to Problem 146AP

Solution:

(a) $0.307\text{ g}$

(b) $0.410\text{ g}$

(c) $12.08\text{ g}$, $90.2\%$

Explanation of Solution

a) The number of salicylic acid is required to produce 0.400 g of aspirin.

The number of moles is given by the following expression:

$n=\frac{\text{given mass}\left(m\right)}{\text{molar mass}\left(M\right)}$

Since molar ratio of salicylic acid to aspirin is $1:1$, $n_{\text{aspirin}}=n_{\text{salicylic acid}}$.

The above expression can be rewritten as

$n\times \text{molar mass}\left(M\right)=\text{given mass}\left(m\right)$

So, the mass of salicylic acid is given by the following expression:

$n_{\text{aspirin}}\times \left(M_{\text{salicylic acid}}\right)=\left(m_{\text{salicylic acid}}\right)$

The above expression can be rewritten as

$\frac{m_{\text{aspirin}}}{M_{\text{aspirin}}}\times \left(M_{\text{salicylic acid}}\right)=\left(m_{\text{salicylic acid}}\right)$

Substitute $0.400\text{ g}$ for $m_{\text{aspirin}}$, $180.15\text{ g}/\text{mol}$ for $M_{\text{aspirin}}$, and $138.12\text{ g}/\text{mol}$ for $M_{\text{salicylic acid}}$ in the above equation

$\begin{array}{c}\frac{0.400\text{ g}}{180.15\text{ g}/\text{mol}}\times \left(138.12\text{ g}/\text{mol}\right)=\left(m_{\text{salicylic acid}}\right)\\ \frac{55.248{\text{ g}}^2/\text{mol}}{180.15\text{ g}/\text{mol}}=\left(m_{\text{salicylic acid}}\right)\\ 0.307\text{ g}=\left(m_{\text{salicylic acid}}\right)\end{array}$

Hence, the mass of salicylic acid is $0.307\text{ g}$.

b) The amount of salicylic acid needed if only 74.9% of salicylic acid is converted to aspirin.

The amount of salicylic acid used was $0.307\text{ g}$.

Since 74.9% of salicylic acid is converted to aspirin, the molar ratio of aspirin to that of salicylic acid is $1:0.749$, as the amount of aspirin produced is same in the given reaction.

The amount salicylic acid used is calculated as

$\begin{array}{c}\text{Amount}\text{of}\text{aspirin}\text{used}=\frac{1}{0.749}\times 0.307\text{ g}\\ =\text{0}\text{.410 g}\end{array}$

Hence, mass of salicylic acid required is $\text{0}\text{.410 g}$.

c)The theoretical yield of aspirin and the percent yield if only 10.9 g of aspirin is produced.

Mass of salicylic acid $=9.26\text{ g}$

Mass of acetic anhydride $=8.54\text{ g}$

Mass of aspirin $=10.9\text{ g}$

Since the molar ratio of salicylic acid to aspirin is $1:1$, $n_{\text{aspirin}}=n_{\text{salicylic acid}}$.

The number of moles of salicylic acidis given by the following expression:

$n_{\text{salicylic acid}}=\frac{m_{\text{salicylic acid}}}{M_{\text{salicylic acid}}}$

Substitute $9.26\text{ g}$ for $m_{\text{salicylic acid}}$ and $138.12\text{ g}/\text{mol}$ for $M_{\text{salicylic acid}}$ in the above equation

$\begin{array}{c}{n}_{\text{salicylic acid}}=\frac{9.26\text{ g}}{138.12\text{ g}/\text{mol}}\\ =0.06704\text{ mol}\end{array}$

Since molar ratio of acetic anhydride to aspirin is also $1:1$, $n_{\text{aspirin}}=n_{\text{acetic anhydride}}$.

The number of moles of acetic anhydrideis given by the following expression:

$n_{\text{acetic anhydride}}=\frac{m_{\text{acetic anhydride}}}{M_{\text{acetic anhydride}}}$

Substitute $8.54\text{ g}$ for $m_{\text{acetic anhydride}}$ and $102.09\text{ g}/\text{mol}$ for $M_{\text{acetic anhydride}}$ in the above equation

$\begin{array}{c}{n}_{\text{aspirin}}=\frac{8.54\text{ g}}{102.09\text{ g}/\text{mol}}\\ =0.08365\text{ mol}\end{array}$

Therefore, it is clear that salicylic acid is a limiting reactant. So, mass of aspirin produced is calculated as

$\begin{array}{c}{n}_{\text{aspirin}}\times M_{\text{aspirin}}=m_{\text{aspirin}}\\ n_{\text{salicylic acid}}\times M_{\text{aspirin}}=m_{\text{aspirin}}\end{array}$

Substitute $0.06704\text{ mol}$ for $n_{\text{salicylic acid}}$ and $180.15\text{ g}/\text{mol}$ for $M_{\text{aspirin}}$ in the above equation

$\begin{array}{c}0.06704\text{ mol}\times 180.15\text{ g}/\text{mol}=m_{\text{aspirin}}\\ 12.08\text{ g}=m_{\text{aspirin}}\end{array}$

Therefore, theoretical yield or actual yield is $12.08\text{ g}$.

The percent yield of the aspirin is given by the following expression:

Percent yield is given by = $\frac{\text{observed yield}}{\text{actual yield}}\times 100$

Substitute $12.08\text{ g}$ for actual yield and $10.9\text{ g}$ for $\text{observed yield}$ in the above equation

$\begin{array}{c}\%\text{ yield}=\frac{10.9\text{ g}}{12.08\text{ g}}\times 100\\ =0.902\times 100\\ =90.2\%\end{array}$

Hence, the theoretical yield should be $12.08\text{ g}$ and the percent yield is $90.2\%$.