Q29 E - Chemistry (OpenStax)

Question

Ethylene can be produced by the pyrolysis of ethane: 

\[{{\rm{C}}_{\rm{2}}}{{\rm{H}}_{\rm{6}}}\to{{\rm{C}}_{\rm{2}}}{{\rm{H}}_{\rm{4}}}{\rm{+}}{{\rm{H}}_{\rm{2}}}\]

How many kilograms of ethylene is produced by the pyrolysis of 1.000 ×10³ kg of ethane, assuming a 100.0%yield?

Step-by-Step Solution

Answer

932.888kg of ethylene is produced by pyrolysis of 1.000 ×10³ kg of ethane

Step 1: Definition of Pyrolysis

Pyrolysis is the thermal degradation of materials in an inert atmosphere at high temperatures. It entails a chemical composition shift.

Step 2: Determining the empirical formula of silver and carbon

Ethane's molar mass is:

\begin{aligned}{\rm{M}}\left({{{\rm{C}}_{\rm{2}}}{{\rm{H}}_{\rm{6}}}}\right){\rm{=2Ar(C)+6Ar(H)}}\\{\rm{=212}}{\rm{.01+61}}{\rm{.008}}\\{\rm{=30}}{\rm{.07gmo}}{{\rm{l}}^{{\rm{-1}}}}\end{aligned}

The quantity of ethane (in moles) is then:

\begin{aligned}{\rm{n(\;ethane\;)=}}\frac{{{\rm{m(\;ethane\;)}}}}{{{\rm{M(\;ethane\;)}}}}\\{\rm{=}}\frac{{\left({{\rm{1}}\times{\rm{1}}{{\rm{0}}^{\rm{6}}}{\rm{g}}}\right)}}{{\left({{\rm{30}}{\rm{.07gmo}}{{\rm{l}}^{{\rm{-1}}}}}\right)}}\\{\rm{=33,255}}{\rm{.7mol}}\end{aligned}

n( ethane) = n(ethene)

                 = 33,255.7mol

The molar mass of ethene, C₂H₄, is as follows:

\begin{aligned}{\rm{M}}\left({{{\rm{C}}_{\rm{2}}}{{\rm{H}}_{\rm{4}}}}\right){\rm{=2Ar(C)+4Ar(C)}}\\{\rm{=212}}{\rm{.01+41}}{\rm{.008}}\\{\rm{=28}}{\rm{.05gmo}}{{\rm{l}}^{{\rm{-1}}}}\end{aligned}

This indicates that the ethene mass is

\begin{aligned}{\rm{m\;(ethene\;)=}}{{\rm{M}}_{ethene}}\times{\rm{n}}{{\rm{\;}}_{{\rm{ethene}}}}\\{\rm{=28}}{\rm{.05gmo}}{{\rm{l}}^{-1}}\times{\rm{33,255}}{\rm{.7mol}}\\{\rm{=932888g}}\\{\rm{=932}}{\rm{.888kg}}{\rm{.\;}}\end{aligned}