Ethers (general formula .R-O-R^') have many important uses. Until recently, methyl tert-butyl et

step 1 MTBE which is an additive in gasoline has the structure O -C -H -3 this can be synthesized by ad

Ethers (general formula .R-O-R^') have many important uses....

Ethers (general formula $\left.\mathrm{R}-\mathrm{O}-\mathrm{R}^{\prime}\right)$ have many important uses. Until recently, methyl tert-butyl ether (MTBE, below) was used as an octane booster and fuel additive for gasoline. It increases the oxygen content of the fuel, which reduces CO emissions. MTBE is synthesized by the catalyzed reaction of 2 -methylpropene with methanol. (a) Write a balanced equation for the synthesis of MTBE. (Hint: Alcohols add to alkenes similarly to the way water does.) (b) If the government required that auto fuel mixtures contain $2.7 \%$ oxygen by mass to reduce CO emissions, how many grams of MTBE would have to be added to each $100 . \mathrm{g}$ of gasoline? (c) How many liters of MTBE would be in each liter of fuel mixture? (The density of both gasoline and $\mathrm{MTBE}$ is $0.740 \mathrm{~g} / \mathrm{mL}$.) (d) How many liters of air $\left(21 \% \mathrm{O}_{2}\right.$ by volume $)$ are needed at $24^{\circ} \mathrm{C}$ and 1.00 atm to fully combust $1.00 \mathrm{~L}$ of MTBE?

Key Concepts

Acid-Catalyzed Addition Reactions

This concept involves the mechanism in which an acid catalyst is used to activate an alkene towards nucleophilic attack. The alkene reacts with a nucleophile such as an alcohol, leading to addition across the double bond. This type of reaction is foundational in organic synthesis and illustrates how catalysts can lower the energy barrier of a reaction, leading to the formation of new bonds under milder conditions.

Synthetic Methods for Ethers

Ethers can be synthesized by the addition of alcohols to alkenes, among other methods. This method utilizes the reactivity of alkenes with nucleophilic alcohols under acid-catalyzed conditions to form the ether linkage (R–O–R'). Understanding this synthesis pathway is important in organic chemistry for constructing compounds with oxygen bridges, which are prevalent in many industrial applications.

Stoichiometry

Stoichiometry is the quantitative study of reactants and products in a chemical reaction. In an organic synthesis reaction, it is used to determine the exact amounts of substances required or produced. Mastery of stoichiometry is essential for balancing chemical equations, scaling reactions, and optimizing yields in both laboratory and industrial settings.

Mass Percentage Calculations

Mass percentage calculations involve determining the proportion of a specific element or functional group within a compound relative to the compound's total mass. This concept is critical when adjustments to the composition of a mixture are needed, such as ensuring that a fuel mixture contains a required percentage of a particular element to achieve desired combustion properties.

Density and Volume Conversions

Density and volume conversions form the bridge between mass measurements and volumetric analysis. In many chemical applications, knowing the density of a substance allows for the conversion between grams and milliliters or liters. This is particularly important in contexts where precise measurements of liquids are required, such as in fuel formulations or reagent handling.

Ideal Gas Law

The ideal gas law (PV = nRT) is a fundamental relationship in chemistry that relates a gas's pressure, volume, temperature, and number of moles. This principle is used to calculate the conditions under which a gas will react or to determine the volume of gas produced or required in a chemical reaction, such as during combustion. It is an essential tool for understanding and predicting the behavior of gases under various conditions.

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