Question 3.9: CALCULATING A YIELD IN GRAMS, GIVEN A PERCENT YIELD Diethyl ...
CALCULATING A YIELD IN GRAMS, GIVEN A PERCENT YIELD
Diethyl ether (C_{4}H_{10}O), the “ether” used medically as an anesthetic, is prepared commercially by treatment of ethyl alcohol (C_{2}H_{6}O) with an acid. How many grams of diethyl ether would you obtain from 40.0 g of ethyl alcohol if the percent yield of the reaction is 87%?
\underset{Ethyl alcohol}{2 C_{2}H_{6}O(l)} \underrightarrow{Acid} \underset{Diethyl ether}{C_{4}H_{10}O(l)} + H_{2}O(l)STRATEGY
Treat this as a typical stoichiometry problem to find the amount of diethyl ether that can theoretically be formed from 40.0 g of ethyl alcohol, and then multiply the answer by 87% to find the amount actually formed.
First, calculate the molar masses of the reactant and product:
Ethylalcohol, C_{2}H_{6}O: Molec. mass = (2 × 12.0 amu) + (6 × 1.0 amu) + 16.0 amu
= 46.0 amu
Molar mass of ethyl alcohol = 46.0 g/mol
Diethyl ether, C_{4}H_{10}O: Molec.mass = (4 × 12.0 amu) + (10 × 1.0 amu) + 16.0 amu
= 74.0 amu
Molar mass of diethyl ether = 74.0 g/mol
Next, find how many moles of ethyl alcohol are in 40.0 g by using molar mass as a conversion factor:
40.0 \cancel{g ethyl alcohol} × \frac{1 mol ethyl alcohol}{46.0 \cancel{g ethyl alcohol}} = 0.870 mol ethyl alcohol
Because we started with 0.870 mol of ethyl alcohol, and because the balanced equation indicates that 2 mol of ethyl alcohol yield 1 mol of diethyl ether, we can theoretically obtain 0.435 mol of product:
0.870 \cancel{mol ethyl alcohol} × \frac{1 mol diethyl ether}{2 \cancel{mol ethyl alcohol}} = 0.435 mol diethyl ether
We therefore need to find how many grams of diethyl ether are in 0.435 mol, using molar mass as the conversion factor:
0.435 \cancel{mol diethyl ether} × \frac{74.0 g diethyl ether}{1 \cancel{mol diethyl ether}} = 32.2 g diethyl ether
Finally, we have to multiply the theoretical amount of product by the observed yield (87% = 0.87 ) to find how much diethyl ether is actually formed:
32.2 g diethyl ether × 0.87 = 28 g diethyl ether