Q37 E - Chemistry (OpenStax)

Question

MTBE, Methyl tert-butyl ether, CH₃OC(CH₃)₃, is used as an oxygen source in oxygenated gasolines. MTBE is manufactured by reacting 2-methylpropene with methanol. 

(a) Using Lewis structures, write the chemical equation representing the reaction.

(b) What volume of methanol, density 0.7915 g/mL, is required to produce exactly 1000 kg of MTBE, assuming a 100% yield? 

Step-by-Step Solution

Answer

(a)

(b) The final volume of methanol is 475.5 L.

Step 1: a) chemical equation

Step 2: b) Volume of methanol

 Let's get information from MTBE.

We have its mass of 1000kg, and we know its molecular formula - C₅H₁₂O, which we can use to count molar mass.

The molar mass is:

M(MBTE) = 5Ar (C) +12Ar(H) +Ar(O) =88.15gmol^-1                   

Now we have the mass and molar mass which gives us n:

n(MTBE)=m(MTBE)/M(MTBE) = (1,000,000g)/(88.15gmol^-1) =11,744.5mol

n(methanol) = n(MTBE) =11,744.5 mol             

The mass of methanol is required for calculations.

\begin{aligned}m(methanol)=n(methanol)\times M(methanol)\\=(11,744.5\;mol)\times\left({32.04gmo{l^{-1}}}\right)\\=376,317\;g\end{aligned}

Then, volume is calculated from mass and density as given in our textbook.

  \begin{aligned}V(methanol)=m(methanol)/\rho(methanol)\\=(376,317\;g)/(0.7915gm{L^{-1}})\\=475,558\;c{m^3}\\=475.558\;L.\end{aligned}

Step 3: Final answer

V= 475.5 L