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Chapter 9: Q77E (page 511)

Ethanol, C2H5OH,is produced industrially from ethylene, C2H4, by the following sequence of reactions:

\begin{aligned}{\rm{3}}{{\rm{C}}_{\rm{2}}}{{\rm{H}}_{\rm{4}}}{\rm{+2}}{{\rm{H}}_{\rm{2}}}{\rm{S}}{{\rm{O}}_{\rm{4}}}\to{{\rm{C}}_{\rm{2}}}{{\rm{H}}_{\rm{5}}}{\rm{HS}}{{\rm{O}}_{\rm{4}}}{\rm{+(}}{{\rm{C}}_{\rm{2}}}{{\rm{H}}_{\rm{5}}}{{\rm{)}}_{\rm{2}}}{\rm{S}}{{\rm{O}}_{\rm{4}}}\\{{\rm{C}}_{\rm{2}}}{{\rm{H}}_{\rm{5}}}{\rm{HS}}{{\rm{O}}_{\rm{4}}}{\rm{ +(}}{{\rm{C}}_{\rm{2}}}{{\rm{H}}_{\rm{5}}}{{\rm{)}}_{\rm{2}}}{\rm{S}}{{\rm{O}}_{\rm{4}}}{\rm{+3}}{{\rm{H}}_{\rm{2}}}{\rm{O}}\to{\rm{3}}{{\rm{C}}_{\rm{2}}}{{\rm{H}}_{\rm{5}}}{\rm{OH + 2}}{{\rm{H}}_{\rm{2}}}{\rm{S}}{{\rm{O}}_{\rm{4}}} \end{aligned}

What volume of ethylene at STP is required to produce 1000 metric tons (1000kg) of ethanol if the overall yield of ethanol is 90.1%?

Short Answer

Expert verified

The volume of ethylene is obtained as 5.4脳105 L.

Step by step solution

01

Define Gas

A gas is made up of particles with no definite volume or structure

02

Evaluating the mass of the ethanol produced

The mass of the ethanol produced is:

1000kg = 1脳106 g

The overall yield of ethanol is 90.1%.

The mass of the overall liquid produced is:

\(\frac{{{\rm{90}}{\rm{.1 \% }}}}{{100}}{\rm{ \times1\times1}}{{\rm{0}}^{\rm{6}}}{\rm{ g = 1}}{\rm{.1099 \times1}}{{\rm{0}}^{\rm{6}}}{\rm{ g}}\)

So,the mass of the ethanol produced is

\({\rm{1}}{\rm{.1099\times1}}{{\rm{0}}^{\rm{6}}}{\rm{ g}}\).

03

Evaluating the volume

The following conversions must be made to get from the mass of ethanol to the volume of ethylene:

\({\rm{Mass of }}{{\rm{C}}_{\rm{2}}}{{\rm{H}}_{\rm{5}}}{\rm{OH }} \to {\rm{ Moles of }}{{\rm{C}}_{\rm{2}}}{{\rm{H}}_{\rm{5}}}{\rm{OH }} \to {\rm{ Mass of }}{{\rm{C}}_{\rm{2}}}{{\rm{H}}_{\rm{4}}}{\rm{ }} \to {\rm{ Volume of }}{{\rm{C}}_{\rm{2}}}{{\rm{H}}_{\rm{4}}}\)

So, the first two conversions are:

\({\rm{1}}{\rm{.1099 \times 1}}{{\rm{0}}^{\rm{6}}}{\rm{ g \times }}\frac{{{\rm{1 mol }}{{\rm{C}}_{\rm{2}}}{{\rm{H}}_{\rm{5}}}{\rm{OH}}}}{{{\rm{46}}{\rm{.07 }}{{\rm{C}}_{\rm{2}}}{{\rm{H}}_{\rm{5}}}{\rm{OH}}}}{\rm{ \times }}\frac{{{\rm{1 mol }}{{\rm{C}}_{\rm{2}}}{{\rm{H}}_{\rm{4}}}}}{{{\rm{1 mol }}{{\rm{C}}_{\rm{2}}}{{\rm{H}}_{\rm{5}}}{\rm{OH}}}}{\rm{ = 2}}{\rm{.41 \times 1}}{{\rm{0}}^{\rm{4}}}{\rm{ mol }}{{\rm{C}}_{\rm{2}}}{{\rm{H}}_{\rm{4}}}\)

Then, using the ideal gas law as:

At, \(\begin{array}{c}{\rm{STP, T = 273 K}}\\{\rm{P = 1 atm}}\end{array}\)

\(\begin{array}{c}{{\rm{V}}_{{{\rm{C}}_{\rm{2}}}{{\rm{H}}_{\rm{2}}}}}{\rm{ = }}{\left( {\frac{{{\rm{nRT}}}}{{\rm{P}}}} \right)_{{{\rm{C}}_{\rm{2}}}{{\rm{H}}_{\rm{2}}}}}\\{\rm{ = }}\frac{{{\rm{2}}{\rm{.41 \times 1}}{{\rm{0}}^{\rm{4}}}{\rm{\;mol \times 0}}{\rm{.08206\;L\;atm\;mo}}{{\rm{l}}^{{\rm{ - 1}}}}{\rm{\;}}{{\rm{K}}^{{\rm{ - 1}}}}{\rm{ \times 273\;K}}}}{{{\rm{1\;atm}}}}\\{\rm{ = 5}}{\rm{.4 \times 1}}{{\rm{0}}^{\rm{5}}}{\rm{\;L}}\end{array}\)

Therefore, the volume is: \({\rm{5}}{\rm{.4 \times 1}}{{\rm{0}}^{\rm{5}}}{\rm{\;L}}\).

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Most popular questions from this chapter

Question: Under which of the following sets of conditions does a real gas behave most like an ideal gas, and for which conditions is a real gas expected to deviate from ideal behaviour? Explain.

(a) high pressure, small volume

(b) high temperature, low pressure

(c) low temperature, high pressure

Consider this scenario and answer the following questions: On a mid-August day in the north-eastern United States, the following information appeared in the local newspaper: atmospheric pressure at sea level 29.97 in. Hg,1013.9 mbar. (a) What was the pressure in kPa? (b) The pressure near the seacoast in the north-eastern United States is usually reported near 30.0 in. During a hurricane, the pressure may fall to near 28.0 in. Calculate the drop in pressure in torr.

A 2.50Lsample of a colorless gas at STP decomposed to give 2.50L of N2 and 1.25L of O2 at STP. What is colorless gas?

Question: When two cotton plugs, one moistened with ammonia and the other with hydrochloric acid, are simultaneously inserted into opposite ends of a glass tube that is 87.0 cm long, a white ring of \({\rm{N}}{{\rm{H}}_{\rm{4}}}{\rm{Cl}}\) forms where gaseous \({\rm{N}}{{\rm{H}}_{\rm{3}}}\) and gaseous \({\rm{HCl}}\) first come into contact. (Hint: Calculate the rates of diffusion for both \({\rm{N}}{{\rm{H}}_{\rm{3}}}\) and \({\rm{HCl}}\), and find out how much faster \({\rm{N}}{{\rm{H}}_{\rm{3}}}\) diffuses than \({\rm{HCl}}\).) \({\rm{N}}{{\rm{H}}_{\rm{3}}}{\rm{(g) + HCl(g)}} \to {\rm{N}}{{\rm{H}}_{\rm{4}}}{\rm{Cl(s)}}\)

At approximately what distance from the ammonia moistened plug does this occur?

A sample of a compound of xenon and fluorine was confined in a bulb with a pressure of 18 torr. Hydrogen was added to the bulb until the pressure was 72 torr. The passage of an electric spark through the mixture produced Xe and HF. After the HF was removed by reaction with solid KOH, the final pressure of xenon and unreacted hydrogen in the bulb was 36torr. What is the empirical formula of the xenon fluoride in the original sample? (Note: Xenon fluorides contain only one xenon atom per molecule.)
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