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Chapter 2: Problem 42

In a combustion reaction, \(46.0 \mathrm{~g}\) of ethanol reacts with \(96.0 \mathrm{~g}\) of oxygen to produce water and carbon dioxide. If \(54.0 \mathrm{~g}\) of water is produced, what mass of carbon dioxide is produced?

Short Answer

Expert verified
In the given combustion reaction, we first determine the limiting reactant, which is ethanol. Next, we use stoichiometry to find the mass of CO2 produced: Mass of CO2= 2 * n_(limiting reactant) * M_(CO2). Finally, we subtract the mass of water formed (54.0 g) from the total mass of products to find the mass of CO2 produced in the reaction, which is \(88.0 \mathrm{~g}\) of CO2.

Step by step solution

01

Write and balance the combustion reaction

Ethanol, C2H5OH, reacts with oxygen, O2, to produce water, H2O, and carbon dioxide, CO2. The balanced reaction is given by: C2H5OH + 3 O2 -> 2 CO2 + 3 H2O
02

Find the limiting reactant

To find the limiting reactant, calculate the number of moles of ethanol and oxygen. To do this, divide the mass given (in grams) by the molar mass of each substance. \(n_{C2H5OH} = \frac{46.0\mathrm{~g}}{46.07\mathrm{~g/mol}}\) \(n_{O2} = \frac{96.0\mathrm{~g}}{32.00\mathrm{~g/mol}}\) Compare the mole-to-coefficient ratio for ethanol and oxygen: \(\frac{n_{C2H5OH}}{1} = \frac{46.0/46.07}{1}\) \(\frac{n_{O2}}{3} = \frac{96.0/32.00}{3}\) The limiting reactant is the one with a smaller mole-to-coefficient ratio.
03

Determine the mass of carbon dioxide produced

Use the limiting reactant, mole-to-coefficient relationship, and molar mass to calculate the mass of carbon dioxide produced: \(n_{CO2} = 2 * n_{limiting~reactant}\) Mass of CO2 = \(n_{CO2} * M_{CO2}\) Where M refers to the molar mass of a substance. Finally, subtract the mass of water produced from the mass of carbon dioxide and water to find the mass of carbon dioxide produced.
04

Calculate the mass of carbon dioxide produced

Use your findings in Steps 2 and 3 to calculate the mass of carbon dioxide produced: Determine the limiting reactant, then find the mass of the carbon dioxide produced. And finally, subtract the mass of water formed to find the mass of carbon dioxide produced in the reaction.

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