Chapter 2, Problem 85QRT

(a)

Interpretation Introduction

Interpretation:

The amount of aspirin, sodium bicarbonate and citric acid present in the tablet has to be calculated.

Explanation of Solution

The molecular formula of aspirin is ${\text{C}}_{\text{9}}{\text{H}}_{\text{8}}{\text{O}}_{\text{4}}$.

The molecular formula of sodium carbonate is ${\text{NaHCO}}_{\text{3}}$.

The molecular formula of citric acid is ${\text{C}}_{\text{6}}{\text{H}}_{\text{8}}{\text{O}}_{\text{7}}$.

Mass of carbon $\text{=}\text{12}\text{.0107}\text{g/mol}$.

Mass of hydrogen $\text{=}\text{1}\text{.0079}\text{g/mol}$.

Mass of oxygen $\text{=}\text{15}\text{.9994}\text{g/mol}$.

Mass of sodium $\text{=}22.98977\text{g/mol}$

The molar mass of aspirin

  $\text{=}\text{(}\text{9}\text{×}\text{12}\text{.0107}\text{g/mol)}\text{+}\text{(}\text{8}\text{×}\text{1}\text{.0079}\text{g/mol}\text{)}\text{+}\text{(}\text{4}\text{×}\text{15}\text{.994}\text{g/mol}\text{)}\text{=}\text{180}\text{.1571}\text{g/mol}$.

The molar mass of sodium bicarbonate

  $\text{=}\text{22}\text{.989}\text{g/mol}\text{+}\text{1}\text{.0079}\text{g/mol}\text{+}\text{12}\text{.0107}\text{g/mol}\text{+}\text{(3×15}\text{.9994}\text{g/mol)}\text{=}\text{84}\text{.0066}\text{g/mol}$.

The molar mass of citric acid

  $\text{=}\text{(}6\text{×}\text{12}\text{.0107}\text{g/mol)}\text{+}\text{(}\text{8}\text{×}\text{1}\text{.0079}\text{g/mol}\text{)}\text{+}\text{(}7\text{×}\text{15}\text{.994}\text{g/mol}\text{)}\text{=}192.1232\text{g/mol}$.

Then,

The amount of aspirin

  $\text{=}\text{324}\text{mg}{\text{C}}_{\text{9}}{\text{H}}_{\text{8}}{\text{O}}_{\text{4}}\text{×}\frac{\text{1}\text{g}{\text{C}}_{\text{9}}{\text{H}}_{\text{8}}{\text{O}}_{\text{4}}}{\text{100}\text{mg}{\text{C}}_{\text{9}}{\text{H}}_{\text{8}}{\text{O}}_{\text{4}}}\text{×}\frac{\text{1}\text{mol}{\text{C}}_{\text{9}}{\text{H}}_{\text{8}}{\text{O}}_{\text{4}}}{\text{180}\text{.1571}\text{g}{\text{C}}_{\text{9}}{\text{H}}_{\text{8}}{\text{O}}_{\text{4}}}\text{=}\text{0}\text{.00180}\text{mol}{\text{C}}_{\text{9}}{\text{H}}_{\text{8}}{\text{O}}_{\text{4}}$.

The amount of sodium bicarbonate

  $\text{=}\text{1904}\text{mg}{\text{NaHCO}}_{\text{3}}\text{×}\frac{\text{1}\text{g}{\text{NaHCO}}_{\text{3}}}{\text{1000}\text{mg}{\text{NaHCO}}_{\text{3}}}\text{×}\frac{\text{1}\text{mol}{\text{NaHCO}}_{\text{3}}}{\text{84}\text{.0066}\text{g}{\text{NaHCO}}_{\text{3}}}\text{=}\text{0}\text{.02266}\text{mol}{\text{NaHCO}}_{\text{3}}$.

The amount of citric acid

  $\text{=}\text{1000}\text{mg}{\text{C}}_{\text{6}}{\text{H}}_{\text{8}}{\text{O}}_{\text{7}}\text{×}\frac{\text{1}\text{g}{\text{C}}_{\text{6}}{\text{H}}_{\text{8}}{\text{O}}_{\text{7}}}{\text{1000}\text{mg}{\text{C}}_{\text{6}}{\text{H}}_{\text{8}}{\text{O}}_{\text{7}}}\text{×}\frac{\text{1}\text{mol}{\text{C}}_{\text{6}}{\text{H}}_{\text{8}}{\text{O}}_{\text{7}}}{\text{192}\text{.1232}\text{g}{\text{C}}_{\text{6}}{\text{H}}_{\text{8}}{\text{O}}_{\text{7}}}\text{=}\text{0}\text{.005205}\text{mol}{\text{C}}_{\text{6}}{\text{H}}_{\text{8}}{\text{O}}_{\text{7}}$.

(b)

Interpretation Introduction

Interpretation:

If one tablet is taken, then the number of aspirin molecules consumed has to be given.

Explanation of Solution

The molecular formula of aspirin is ${\text{C}}_{\text{9}}{\text{H}}_{\text{8}}{\text{O}}_{\text{4}}$.

The molar mass of aspirin

  $\text{=}\text{(}\text{9}\text{×}\text{12}\text{.0107}\text{g/mol)}\text{+}\text{(}\text{8}\text{×}\text{1}\text{.0079}\text{g/mol}\text{)}\text{+}\text{(}\text{4}\text{×}\text{15}\text{.994}\text{g/mol}\text{)}\text{=}\text{180}\text{.1571}\text{g/mol}$.

Then the number of molecules is:

$\text{0}\text{.00180}\text{mol}{\text{C}}_{\text{9}}{\text{H}}_{\text{8}}{\text{O}}_{\text{4}}\text{×}\frac{\text{6}{\text{.022×10}}^{\text{23}}{\text{C}}_{\text{9}}{\text{H}}_{\text{8}}{\text{O}}_{\text{4}}\text{molecules}}{\text{1}\text{mol}{\text{C}}_{\text{9}}{\text{H}}_{\text{8}}{\text{O}}_{\text{4}}}\text{=}\text{1}\text{.08}\text{×}{\text{10}}^{\text{21}}{\text{C}}_{\text{9}}{\text{H}}_{\text{8}}{\text{O}}_{\text{4}}\text{molecules}$.