Chapter 3.4, Problem 20PP

Interpretation Introduction

Interpretation:

The percentage by mass of hydrogen in the compound that is formed needs to be determined.

Concept introduction:

Formula to calculate the moles of element,

$\text{Moles}\text{of}\text{Element = }\frac{\text{Mass}\text{of}\text{Element}}{\text{Molar}\text{Mass}\text{of}\text{Element}}$

The mass percentage is defined as the percentage of component present in it. The mass percentage of the element is the mass of element divided by the total mass of the compound and multiplied by 100.

$\text{Mass percentage=}\frac{\text{mass}\text{of}\text{element}}{\text{mass}\text{of}\text{total}\text{compound}}\text{×100}$

Answer to Problem 20PP

The required percentage is $\text{5\%}$.

Explanation of Solution

Given information:

Mass of hydrogen $\text{=}\text{1}\text{g}$

Mass of fluorine $\text{=}\text{19}\text{g}$

Molar mass of hydrogen $\text{= 2 g/mole}$

Molar mass of fluorine $\text{= 38 g/mole}$

First calculate the moles of hydrogen and fluorine by using the formula, $\text{Moles}\text{of}\text{Element = }\frac{\text{Mass}\text{of}\text{Element}}{\text{Molar}\text{Mass}\text{of}\text{Element}}$

${\text{Moles of H}}_{\text{2}}\text{=}\frac{\text{Mass}\text{of}{\text{H}}_{\text{2}}}{\text{Molar}\text{Mass}\text{of}{\text{H}}_{\text{2}}}\text{=}\frac{\text{1}\text{g}}{\text{2}\text{g/mole}}\text{= 0}\text{.5}\text{moles}$

${\text{Moles of F}}_{\text{2}}\text{=}\frac{\text{Mass}\text{of}{\text{F}}_{\text{2}}}{\text{Molar}\text{Mass}\text{of}{\text{F}}_{\text{2}}}\text{=}\frac{\text{19}\text{g}}{\text{38}\text{g/mole}}\text{= 0}\text{.5}\text{moles}$

Now calculate the moles of HF by using the balance chemical reaction, ${\text{H}}_2+F_2\to 2HF$

As $\text{1}\text{mole}$ of ${\text{H}}_2$ reacts to give $\text{2}\text{moles}$ of $\text{HF}$

Thus, $0.5\text{mole}$ of ${\text{H}}_2$ reacts to give $\text{0}\text{.5×2=1}\text{mole}$ of $\text{HF}$

Lastly, calculate the percentage by mass of hydrogen by using the formula,

$\text{Mass percentage=}\frac{\text{mass}\text{of}\text{element}}{\text{mass}\text{of}\text{total}\text{compound}}\text{×100}$

Put the values and solve,

$\text{Mass percentage = }\frac{\text{1}}{\text{1+19}}\text{×100 =}\frac{1}{20}\times 100=5\%$

Conclusion

The answer is $\text{5\%}$.