Chapter 24, Problem 64QP

Interpretation Introduction

Interpretation:

The amount of sulfur required to produce $48\text{ million tones}$

of sulphuric acid is to be calculated.

Concept introduction:

The moles of a substance are calculated by the ratio of the mass of the substance to the molar mass of the substance.

$\text{Number of }\text{}\text{moles = }\frac{\text{Given mass}}{\text{Molar mass}}$

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 relationship between $\text{tonn}$ and $\text{lb}$ can be expressed as:

$\text{1}\text{tonn}\text{=}\text{2000}\text{lb}$

To convert $\text{tonn}$ to $\text{lb}$, conversion factor is $\frac{\text{2000 lb}}{\text{1}\text{tonn}}$.

The relationship between $\text{lb}$ and grams can be expressed as:

$\text{1 lb}\text{=}\text{453}\text{.6}\text{g}$.

To convert $\text{lb}$ to grams, conversion factor is $\frac{453.6\text{ g}}{1\text{ lb}}$.

Answer to Problem 64QP

Solution: $\text{1}\text{.4 }\times {\text{ 10}}^{\text{13}}\text{ g S}$

Explanation of Solution

Given information: Volume of ${\text{D}}_{\text{2}}=\text{2L}$.

Pressure, $\text{P=}\text{0}\text{.90 atm}$.

Temperature, $\text{T}={\text{25}}^{\text{o}}\text{C}=\text{298 K}$.

Abundance of ${\text{D}}_{\text{2}}=0.015\%$.

Recovery ${\text{D}}_{\text{2}}=80\%$.

Convert $\text{tonn}$

to $\text{lb}$,

Conversion factor is: $\frac{\text{2000 lb}}{\text{1}\text{tonn}}$

The conversion is as:

${\text{48×10}}^{\text{6}}\text{tonns}{\text{H}}_{\text{2}}{\text{SO}}_{\text{4}}\times \frac{\text{2000 lb}}{\text{1}\text{tonn}}=\text{ 96 }\times {\text{10}}^{\text{9}}\text{lb}$

Convert $\text{lb}$ to $\text{grams}$,

Conversion factor is: $\frac{453.6\text{ g}}{1\text{ lb}}$

The conversion is as:

$\text{96 }\times {\text{10}}^{\text{9}}\cancel{\text{lb}}\times \frac{453.6\text{ g}}{1\cancel{\text{lb}}}=43545.6\times {\text{10}}^{\text{9}}\text{g}$

The molar mass of sulfuric acid $98\text{ g/mol}$.

The number of moles of sulfuric acid is calculated as:

$\text{Number of }\text{}\text{moles = }\frac{\text{Given mass}}{\text{Molar mass}}$

$\begin{array}{c}n=\left(\frac{43545.6\times {\text{10}}^{\text{9}}\cancel{\text{g}}}{98\cancel{\text{g}}\text{/mol}}\right)\\ =444.34\times {10}^9\text{ mol}\end{array}$

$1\text{ mol }$ of ${\text{H}}_{\text{2}}{\text{SO}}_{\text{4}}$ contains $1\text{ mol }$ of $\text{S}$.

The number of moles of $\text{S}$ in $444.34\times {10}^9\text{ mol}$

of ${\text{H}}_{\text{2}}{\text{SO}}_{\text{4}}$ is as:

$\left(\frac{444.34\times {10}^9\cancel{{\text{mol H}}_{\text{2}}{\text{SO}}_{\text{4}}}\times \text{1 mol S}}{1\cancel{{\text{mol H}}_{\text{2}}{\text{SO}}_{\text{4}}}}\right)=444.34\times {10}^9\text{ mol S}$

Now, convert moles to grams,

Mass of 1 mol of sulfur $=32\text{ g/mol}$

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.

$\begin{array}{c}\text{Mass of }444.34\times {10}^9\text{ mol S }=\left(444.34\times {10}^9\cancel{\text{mol}}\text{ S}\times \text{32 g/}\cancel{\text{mol}}\right)\\ =\text{1}\text{.4 }\times {\text{ 10}}^{\text{13}}\text{ g S}\end{array}$

Conclusion

The amount of sulfur required to produce $48\text{ million tones}$ of sulfuric acid is $1.4\times {10}^{13}\text{g S}$.