Question

In a recent year, the United States produced $\mathbf{6}\mathbf{.}\mathbf{26}\mathbf{\times }{\mathbf{10}}^{\mathbf{9}\mathbf{}}\mathbf{Kg}$1,2-dichloroethane and $\mathbf{3}\mathbf{.}\mathbf{73}\mathbf{\times }{\mathbf{10}}^{\mathbf{9}}\mathbf{}\mathbf{Kg}$vinyl chloride. Assuming that all significant quantities of vinyl chloride were produced from 1,2-dichloroethane, what fraction of 1,2-dichloroethane production went into making vinyl chloride? What mass of hydrogen chloride was generated as a by-product?

Short answer

$\mathrm{Fraction} \mathrm{of} 1,2-\mathrm{dichloroethane} \mathrm{reacted} = 94.4\%$.

$\mathrm{Amount}\mathrm{of}\mathrm{HCl}\mathrm{generated}\mathrm{as}\mathrm{a}\mathrm{byproduct} \mathrm{is} 2.18\times {10}^{12}\mathrm{g} \mathrm{of} \mathrm{HCl}.$

Step-by-step solution

Introduction

Vinyl chloride has immense industrial importance in automobiles, furniture, housewares, etc. The manufacturing involves the formation of ethylene dichloride by the reaction of ethene with chlorine followed by heating of 1,2 dichloroethane in the presence of charcoal to give vinyl chloride.

The reaction is as follows:

Solution

According to the chemical equation given:

$$\begin{gathered} 62.5 \mathrm{g} \mathrm{of} \mathrm{vinyl} \mathrm{chloride} \mathrm{is} \mathrm{obtained} \mathrm{from}= 98.95 \mathrm{g} \mathrm{of} 1,2-\mathrm{dichloroethane} \\ 3.73\times {10}^{12} \mathrm{g} \mathrm{of} \mathrm{vinyl} \mathrm{chloride} \mathrm{is} \mathrm{obtained} \mathrm{from}= \frac{98.95}{62.5}\times 3.73\times {10}^{12} \mathrm{g} \mathrm{of} 1,2-\mathrm{dichloroethane} \\ 3.73\times {10}^{12} \mathrm{g} \mathrm{of} \mathrm{vinyl} \mathrm{chloride} \mathrm{is} \mathrm{obtained} \mathrm{from}== 5.91 \times {10}^{12}\mathrm{g} \mathrm{of} 1,2-\mathrm{dichloroethane} \end{gathered}$$

Now to find the fraction of 1,2-dichloroethane that reacted to give $3.73\times {10}^{12}\mathrm{g}$vinyl chloride, the amount reacted must be divided by the total available amount of 1,2-dichloroethane and then multiplied by a hundred.

$\mathrm{Fraction} \mathrm{of} 1,2-\mathrm{dichloroethane} \mathrm{reacted} = \frac{5.91\times {10}^{12}}{6.26\times {10}^{12}}\times 100= 94.4\%$

Hence, 94.4% of the total available 1,2-dichloroethane went into making vinyl chloride.

Step 3: Mass of HCl generated

$$\begin{gathered} 98.95 \mathrm{g} \mathrm{of} 1,2-\mathrm{dichloroethane} \mathrm{reacts} \mathrm{to} \mathrm{give}= 36.5\mathrm{g} \mathrm{of} \mathrm{HCl} \\ 5.91\times {10}^{12}\mathrm{g} \mathrm{of} 1,2-\mathrm{dichloroethane} \mathrm{reacts} \mathrm{to} \mathrm{give}= \frac{36.5}{98.95}\times 5.91\times {10}^{12}\mathrm{g} \mathrm{of} \mathrm{HCl} \\ 5.91\times {10}^{12}\mathrm{g} \mathrm{of} 1,2-\mathrm{dichloroethane} \mathrm{reacts} \mathrm{to} \mathrm{give}= 2.18\times {10}^{12}\mathrm{g} \mathrm{of} \mathrm{HCl} \end{gathered}$$