Chapter 10, Problem 151A

Interpretation Introduction

Interpretation:

The number of moles of each element present in caffeine should be determined.

Concept introduction:

The number of moles of a compound is defined as the ratio of the given mass of the compound to the molar or molecular mass of the compound.

The mathematical expression is given by:

Number of moles = $\frac{\text{given mass of the compound}}{\text{molar mass of the compound}}$

The one mole of any substance is equal to the Avogadro number, i.e., $6.022\times {10}^{23}$ atoms.

Answer to Problem 151A

Number of moles of carbon in ${\text{C}}_{\text{8}}{\text{H}}_{\text{10}}{\text{N}}_{\text{4}}{\text{O}}_{\text{2}}$ = $\text{4}\text{.12}\times {\text{10}}^{-3}\text{ mole}$

Number of moles of hydrogen in ${\text{C}}_{\text{8}}{\text{H}}_{\text{10}}{\text{N}}_{\text{4}}{\text{O}}_{\text{2}}$ = $\text{5}\text{.15}\times {\text{10}}^{-3}\text{ mole}$

Number of moles of nitrogen in ${\text{C}}_{\text{8}}{\text{H}}_{\text{10}}{\text{N}}_{\text{4}}{\text{O}}_{\text{2}}$ = $\text{2}\text{.06}\times {\text{10}}^{-3}\text{ mole}$

Number of moles of oxygen in ${\text{C}}_{\text{8}}{\text{H}}_{\text{10}}{\text{N}}_{\text{4}}{\text{O}}_{\text{2}}$ = $\text{1}\text{.03}\times {\text{10}}^{-3}\text{ mole}$

Explanation of Solution

Molecular formula of caffeine = ${\text{C}}_{\text{8}}{\text{H}}_{\text{10}}{\text{N}}_{\text{4}}{\text{O}}_{\text{2}}$

Molar mass of ${\text{C}}_{\text{8}}{\text{H}}_{\text{10}}{\text{N}}_{\text{4}}{\text{O}}_{\text{2}}$

= $8\left(12.01\text{ g/mole}\right)+10\left(1.0078\text{ g/mole}\right)+4\left(14.01\text{ g/mole}\right)+2\left(15.999\text{ g/mole}\right)$

= $194.2\text{ g/mole}$

Mass of caffeine = $\text{1}\text{.00}\times {\text{10}}^2\text{ mg}$

Convert the mass in mg to g.

Since, 1 g = 1000 mg

Thus, the mass of caffeine in g = $\text{1}\text{.00}\times {\text{10}}^2\text{ mg}\times \frac{1\text{ g}}{1000\text{ mg}}$

= $0.1\text{ g}$

Number of moles of ${\text{C}}_{\text{8}}{\text{H}}_{\text{10}}{\text{N}}_{\text{4}}{\text{O}}_{\text{2}}$ = $\frac{0.1\text{ g}}{\text{194}\text{.2 g/mole}}$

= $\text{5}\text{.15}\times {\text{10}}^{-4}\text{ mole}$

${\text{C}}_{\text{8}}{\text{H}}_{\text{10}}{\text{N}}_{\text{4}}{\text{O}}_{\text{2}}$ contains eight moles of carbon, ten moles of hydrogen, four moles of nitrogen and two moles of oxygen.

Number of moles of carbon in ${\text{C}}_{\text{8}}{\text{H}}_{\text{10}}{\text{N}}_{\text{4}}{\text{O}}_{\text{2}}$ = $\text{5}\text{.15}\times {\text{10}}^{-4}\text{ mole}\times 8$

= $\text{4}\text{.12}\times {\text{10}}^{-3}\text{ mole}$

Number of moles of hydrogen in ${\text{C}}_{\text{8}}{\text{H}}_{\text{10}}{\text{N}}_{\text{4}}{\text{O}}_{\text{2}}$ = $\text{5}\text{.15}\times {\text{10}}^{-4}\text{ mole}\times 10$

= $\text{5}\text{.15}\times {\text{10}}^{-3}\text{ mole}$

Number of moles of nitrogen in ${\text{C}}_{\text{8}}{\text{H}}_{\text{10}}{\text{N}}_{\text{4}}{\text{O}}_{\text{2}}$ = $\text{5}\text{.15}\times {\text{10}}^{-4}\text{ mole}\times 4$

= $\text{2}\text{.06}\times {\text{10}}^{-3}\text{ mole}$

Number of moles of oxygen in ${\text{C}}_{\text{8}}{\text{H}}_{\text{10}}{\text{N}}_{\text{4}}{\text{O}}_{\text{2}}$ = $\text{5}\text{.15}\times {\text{10}}^{-4}\text{ mole}\times 2$

= $\text{1}\text{.03}\times {\text{10}}^{-3}\text{ mole}$