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Chapter 3: Problem 72

Fermentation is a complex chemical process of wine making in which glucose is converted into ethanol and carbon dioxide: $$ \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6} \longrightarrow 2 \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}+2 \mathrm{CO}_{2} $$ glucose ethanol Starting with \(500.4 \mathrm{~g}\) of glucose, what is the maximum amount of ethanol in grams and in liters that can be obtained by this process? (Density of ethanol = \(0.789 \mathrm{~g} / \mathrm{mL} .)\)

Short Answer

Expert verified
The maximum amount of ethanol that can be created from 500.4 g of glucose is approximately 256.3 g or 0.325 L.

Step by step solution

01

Calculate the Molar Masses

First, you need to determine the molar masses for glucose and ethanol. Using the periodic table, the molar mass of glucose, \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\), can be calculated as: \( 6(12.01 \mathrm{g/mol}) + 12(1.01 \mathrm{g/mol}) + 6(16.00 \mathrm{g/mol}) = 180.18 \mathrm{g/mol} \). The molar mass of ethanol, \(\mathrm{C}_{2}\mathrm{H}_{5} \mathrm{OH}\), is: \( 2(12.01 \mathrm{g/mol}) + 6(1.01 \mathrm{g/mol}) + 1(16.00 \mathrm{g/mol}) + 1(1.01 \mathrm{g/mol}) = 46.07 \mathrm{g/mol} \).
02

Calculate Moles of Glucose

Next, convert the mass of glucose to moles using its molar mass. By doing so, \(500.4 \mathrm{g}\) of glucose converts to: \( \frac{500.4 \mathrm{g}}{180.18 \mathrm{g/mol}} = 2.78 \mathrm{mol} \) of glucose.
03

Determine Moles of Ethanol

According to the balanced chemical equation, one mole of glucose (\(\mathrm{C}_{6}\mathrm{H}_{12}\mathrm{O}_{6}\)) yields two moles of ethanol (\(\mathrm{C}_{2}\mathrm{H}_{5}\mathrm{OH}\)). Therefore, \(2.78 \mathrm{mol}\) of glucose will yield: \(2.78 \mathrm{mol} * 2 = 5.56 \mathrm{mol}\) of ethanol.
04

Convert Moles of Ethanol to grams

To convert these moles of ethanol back to grams, multiply by the molar mass of ethanol, yielding: \(5.56 \mathrm{mol} * 46.07 \mathrm{g/mol} = 256.3 \mathrm{g}\) of ethanol.
05

Convert Grams of Ethanol to liters

To convert grams of ethanol to liters, use the density of ethanol as a conversion factor. This yields: \( \frac{256.3 \mathrm{g}}{0.789 \mathrm{g/mL}} = 324.7 \mathrm{mL}\), or equivalently 0.325 L, of ethanol.

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Most popular questions from this chapter

Define the term "mole." What is the unit for mole in calculations? What does the mole have in common with the pair, the dozen, and the gross? What does Avogadro's number represent?

A certain metal oxide has the formula MO, where \(\mathrm{M}\) denotes the metal. A 39.46-g sample of the compound is strongly heated in an atmosphere of hydrogen to remove oxygen as water molecules. At the end, \(31.70 \mathrm{~g}\) of the metal is left over. If \(\mathrm{O}\) has an atomic mass of 16.00 amu, calculate the atomic mass of \(\mathrm{M}\) and identify the element.

Explain clearly what is meant by the statement "The atomic mass of gold is 197.0 amu."

When baking soda (sodium bicarbonate or sodium hydrogen carbonate, \(\mathrm{NaHCO}_{3}\) ) is heated, it releases carbon dioxide gas, which is responsible for the rising of cookies, donuts, and bread. (a) Write a balanced equation for the decomposition of the compound (one of the products is \(\mathrm{Na}_{2} \mathrm{CO}_{3}\) ). (b) Calculate the mass of \(\mathrm{NaHCO}_{3}\) required to produce \(20.5 \mathrm{~g}\) of \(\mathrm{CO}_{2.}\)

Calculate the molar mass of a compound if 0.372 mole of it has a mass of \(152 \mathrm{~g}\).
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