Chapter 4, Problem 4.92QP

(a)

Interpretation Introduction

Interpretation:

The given reaction of Salicylic acid with acetic acid for the formation of aspirin has to be balanced.

Concept Introduction:

Balancing the equation:

• There is a Law for conversion of mass in a chemical reaction i.e., the mass of total amount of the product should be equal to the total mass of the reactants.
• First write the skeletal reaction from the given information.
• Then count the number of atoms of each element in reactants as well as products.
• Place suitable coefficients in front of reactants as well as products until the number of atoms on each side (reactants and products) becomes equal.

Explanation of Solution

Given reaction equation:

  ${\text{C}}_{\text{7}}{\text{H}}_{\text{6}}{\text{O}}_{\text{3(aq)}}{\text{ + CH}}_{\text{3}}{\text{COOH}}_{\text{(aq)}}\stackrel{}{\to }{\text{ C}}_{\text{9}}{\text{H}}_{\text{8}}{\text{O}}_{\text{4(s)}}{\text{ + H}}_{\text{2}}{\text{O}}_{\text{(l)}}$

Balancing the chemical Equation:

Count the number of atoms on each side of the reaction.

Atom	Reactant side	Product side
$\text{C}$	9	9
$\text{H}$	10	10
$\text{O}$	5	5

Yes, the number of atoms present on each side of the reaction is same.  Hence, the given equation is already balanced.

(b)

Interpretation Introduction

Interpretation:

For the given reaction, the number of moles of aspirin that would form from $\text{1}\times {\text{10}}^2\text{ mol}$ of salicylic acid has to be given.

Explanation of Solution

Given reaction equation:

  ${\text{C}}_{\text{7}}{\text{H}}_{\text{6}}{\text{O}}_{\text{3(aq)}}{\text{ + CH}}_{\text{3}}{\text{COOH}}_{\text{(aq)}}\stackrel{}{\to }{\text{ C}}_{\text{9}}{\text{H}}_{\text{8}}{\text{O}}_{\text{4(s)}}{\text{ + H}}_{\text{2}}{\text{O}}_{\text{(l)}}$

From the balanced equation, it is known that one mole of salicylic acid forms one mole of aspirin as product.  That is, ${\text{1 mol C}}_{\text{7}}{\text{H}}_{\text{6}}{\text{O}}_{\text{3}}{\text{ = 1 mol C}}_{\text{9}}{\text{H}}_{\text{8}}{\text{O}}_{\text{4}}$.

For the given moles of salicylic acid, the number of moles of aspirin formed is,

  $\begin{array}{l}1.00\times {10}^2{\text{ mol C}}_{\text{7}}{\text{H}}_{\text{6}}{\text{O}}_{\text{3}}\times \frac{{\text{1 mol C}}_{\text{9}}{\text{H}}_8{\text{O}}_{\text{4}}}{{\text{1 mol C}}_{\text{7}}{\text{H}}_{\text{6}}{\text{O}}_{\text{3}}}=1.00\times {10}^2\text{ mol}\\ \approx 1.00\times {10}^2{\text{ mol C}}_{\text{9}}{\text{H}}_8{\text{O}}_{\text{4}}\end{array}$

Therefore, the number of moles of aspirin produced from given moles of salicylic acid is $1.00\times {10}^2{\text{ mol C}}_{\text{9}}{\text{H}}_8{\text{O}}_{\text{4}}$.

(c)

Interpretation Introduction

Interpretation:

For the given reaction, the amout (in $\text{g}$) of aspirin that would form from $\text{1}\times {\text{10}}^2\text{ mol}$ of salicylic acid has to be given.

Concept Introduction:

Moles:

Mole of the substance is found by dividing the mass of the substance by its molar mass.

  $\text{No}\text{. of moles (n) = }\frac{\text{mass}}{\text{Molar mass}}$

Mass:

Mass of the compound is calculated by mole of the compound multiplied with molar mass of the compound.

  $\text{Mass}\text{=}\text{Molar}\text{mass}\text{×}\text{mole}$

Explanation of Solution

Given reaction equation:

  ${\text{C}}_{\text{7}}{\text{H}}_{\text{6}}{\text{O}}_{\text{3(aq)}}{\text{ + CH}}_{\text{3}}{\text{COOH}}_{\text{(aq)}}\stackrel{}{\to }{\text{ C}}_{\text{9}}{\text{H}}_{\text{8}}{\text{O}}_{\text{4(s)}}{\text{ + H}}_{\text{2}}{\text{O}}_{\text{(l)}}$

From the balanced equation, it is known that one mole of salicylic acid forms one mole of aspirin as product.  That is, ${\text{1 mol C}}_{\text{7}}{\text{H}}_{\text{6}}{\text{O}}_{\text{3}}{\text{ = 1 mol C}}_{\text{9}}{\text{H}}_{\text{8}}{\text{O}}_{\text{4}}$.

For the given moles of salicylic acid, the number of moles of aspirin formed is,

  $\begin{array}{l}1.00\times {10}^2{\text{ mol C}}_{\text{7}}{\text{H}}_{\text{6}}{\text{O}}_{\text{3}}\times \frac{{\text{1 mol C}}_{\text{9}}{\text{H}}_8{\text{O}}_{\text{4}}}{{\text{1 mol C}}_{\text{7}}{\text{H}}_{\text{6}}{\text{O}}_{\text{3}}}=1.00\times {10}^2\text{ mol}\\ \approx 1.00\times {10}^2{\text{ mol C}}_{\text{9}}{\text{H}}_8{\text{O}}_{\text{4}}\end{array}$

Thus, the number of moles of aspirin produced from given moles of salicylic acid is $1.00\times {10}^2{\text{ mol C}}_{\text{9}}{\text{H}}_8{\text{O}}_{\text{4}}$.

The molar mass of aspirin is $\text{180}\text{.158 g/mol}$

Determine the mass of aspirin formed as follows,

  $\begin{array}{l}\text{Mass}\text{=}\text{ Molar}\text{mass}\text{×}\text{mole}\\ \text{= 180}\text{.158 g/mol}\times 1.00\times {10}^2{\text{ mol C}}_{\text{9}}{\text{H}}_8{\text{O}}_{\text{4}}\\ =18015.8\text{ g}\\ \approx 1.80\times {10}^4\text{ g aspirin}\end{array}$

Therefore, the amount of aspirin produced from given moles of salicylic acid is $1.80\times {10}^4\text{ g}$

(d)

Interpretation Introduction

Interpretation:

For the given reaction, the amout (in $\text{g}$) of acetic acid that is required to react completely with the $\text{1}\times {\text{10}}^2\text{ mol}$ of salicylic acid has to be given.

Concept Introduction:

Refer part (c)

Explanation of Solution

Given reaction equation:

  ${\text{C}}_{\text{7}}{\text{H}}_{\text{6}}{\text{O}}_{\text{3(aq)}}{\text{ + CH}}_{\text{3}}{\text{COOH}}_{\text{(aq)}}\stackrel{}{\to }{\text{ C}}_{\text{9}}{\text{H}}_{\text{8}}{\text{O}}_{\text{4(s)}}{\text{ + H}}_{\text{2}}{\text{O}}_{\text{(l)}}$

From the balanced equation, it is known that one mole of salicylic acid and one mole of acetic acid forms one mole of aspirin as product.  That is, ${\text{1 mol C}}_{\text{7}}{\text{H}}_{\text{6}}{\text{O}}_{\text{3}}{\text{ = 1 mol C}}_{\text{9}}{\text{H}}_{\text{8}}{\text{O}}_{\text{4}}$

From the moles of salicylic acid, the moles of acetic acid required is calculated as follows,

  $\begin{array}{l}1.00\times {10}^2{\text{ mol C}}_{\text{7}}{\text{H}}_{\text{6}}{\text{O}}_{\text{3}}\times \frac{{\text{1 mol CH}}_{\text{3}}\text{COOH}}{{\text{1 mol C}}_{\text{7}}{\text{H}}_{\text{6}}{\text{O}}_{\text{3}}}=1.00\times {10}^2\text{ mol}\\ \approx 1.00\times {10}^2{\text{ mol CH}}_{\text{3}}\text{COOH}\end{array}$

Thus, the number of moles of acetic acid that reacts with given moles of salicylic acid is $1.00\times {10}^2{\text{ mol CH}}_{\text{3}}\text{COOH}$.

The molar mass of acetic acid is $\text{60}\text{.052 g/mol}$

Determine the mass of acetic acid required to react is found as follows,

  $\begin{array}{l}\text{Mass}\text{=}\text{ Molar}\text{mass}\text{×}\text{mole}\\ \text{= 60}\text{.052 g/mol}\times 1.00\times {10}^2{\text{ mol CH}}_{\text{3}}\text{COOH}\\ =6005.2\text{ g}\\ \approx \text{ 6}\text{.005}\times {10}^3{\text{ g CH}}_{\text{3}}\text{COOH}\end{array}$

Therefore, the amount of acetic acid required to react with given moles of salicylic acid is $\text{6}\text{.005}\times {10}^3{\text{ g CH}}_{\text{3}}\text{COOH}$

(e)

Interpretation Introduction

Interpretation:

The amount (in $\text{g}$) of product (aspirin) that is produced from calculated mass of acetic acid (from subpart (d)) has to be calculated.

Concept Introduction:

Refer part (c)

Explanation of Solution

Given reaction equation:

  ${\text{C}}_{\text{7}}{\text{H}}_{\text{6}}{\text{O}}_{\text{3(aq)}}{\text{ + CH}}_{\text{3}}{\text{COOH}}_{\text{(aq)}}\stackrel{}{\to }{\text{ C}}_{\text{9}}{\text{H}}_{\text{8}}{\text{O}}_{\text{4(s)}}{\text{ + H}}_{\text{2}}{\text{O}}_{\text{(l)}}$

The amount of acetic acid required to react with given moles of salicylic acid is $\text{6}\text{.005}\times {10}^3{\text{ g CH}}_{\text{3}}\text{COOH}$

The molar mass of acetic acid is $\text{60}\text{.052 g/mol}$

Determine the moles of acetic acid as follows,

$\begin{array}{l}\text{Moles }\text{= }\frac{\text{mass}}{\text{molar mass}}\\ =\frac{\text{6}\text{.005}\times {10}^3{\text{ g CH}}_{\text{3}}\text{COOH}}{\text{60}\text{.052 g/mol}}\\ =100{\text{ moles of CH}}_{\text{3}}\text{COOH}\end{array}$

Thus, the moles of acetic acid is $100{\text{ moles of CH}}_{\text{3}}\text{COOH}$

From the balanced equation, it is known that one mole of salicylic acid and one mole of acetic acid forms one mole of aspirin as product.  That is, ${\text{1 mol CH}}_{\text{3}}{\text{COOH = 1 mol C}}_{\text{9}}{\text{H}}_{\text{8}}{\text{O}}_{\text{4}}$

From the moles of acetic acid, the moles of aspirin formed is calculated as follows,

  $\begin{array}{l}100{\text{ moles of CH}}_{\text{3}}\text{COOH}\times \frac{{\text{1 mol C}}_{\text{9}}{\text{H}}_{\text{8}}{\text{O}}_{\text{4}}}{{\text{1 mol CH}}_{\text{3}}\text{COOH}}=1.00\times {10}^2\text{ mol}\\ \approx 1.00\times {10}^2{\text{ mol C}}_{\text{9}}{\text{H}}_{\text{8}}{\text{O}}_{\text{4}}\end{array}$

Thus, the moles of aspirin is $1.00\times {10}^2{\text{ mol C}}_{\text{9}}{\text{H}}_{\text{8}}{\text{O}}_{\text{4}}$.

The molar mass of aspirin is $\text{180}\text{.158 g/mol}$

Determine the mass of aspirin formed as follows,

  $\begin{array}{l}\text{Mass}\text{=}\text{ Molar}\text{mass}\text{×}\text{mole}\\ \text{= 180}\text{.158 g/mol}\times 1.00\times {10}^2{\text{ mol C}}_{\text{9}}{\text{H}}_8{\text{O}}_{\text{4}}\\ =18015.8\text{ g}\\ \approx 1.80\times {10}^4\text{ g aspirin}\end{array}$

Therefore, the amount of aspirin produced from given moles of salicylic acid is $1.80\times {10}^4\text{ g}$