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The fermentation of glucose produces ethanol and carbon dioxide. Carbon dioxide is a waste product. Balance the symbol equation for the reaction. C_(6)H_(12)O_(6)arrow C_(2)H_(5)OH+CO_(2) Calculate the atom economy for the reaction.

Question

The fermentation of glucose produces ethanol and carbon dioxide. Carbon
dioxide is a waste product.
Balance the symbol equation for the reaction.
C_(6)H_(12)O_(6)arrow C_(2)H_(5)OH+CO_(2)
Calculate the atom economy for the reaction.

The fermentation of glucose produces ethanol and carbon dioxide. Carbon dioxide is a waste product. Balance the symbol equation for the reaction. C_(6)H_(12)O_(6)arrow C_(2)H_(5)OH+CO_(2) Calculate the atom economy for the reaction.

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ClariceElite · Tutor for 8 years

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The balanced chemical equation is \(C_{6}H_{12}O_{6} \rightarrow 2C_{2}H_{5}OH + 2CO_{2}\). The atom economy for the reaction is 51.13%.

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## Step 1: Balancing the Chemical Equation<br />The first step is to balance the chemical equation. The original equation is: \(C_{6}H_{12}O_{6} \rightarrow C_{2}H_{5}OH + CO_{2}\). Balancing the elements Carbon (C), Hydrogen (H) and Oxygen (O), we get: \(C_{6}H_{12}O_{6} \rightarrow 2C_{2}H_{5}OH + 2CO_{2}\). <br /><br />## Step 2: Calculating the Atom Economy<br />The atom economy is a measure of the amount of starting materials that become useful products. It is calculated using the formula:<br /><br />### \(Atom \, Economy = \frac{Molecular \, weight \, of \, desired \, products}{Total \, molecular \, weight \, of \, all \, reactants} \times 100\%\)<br /><br />The molecular weight of glucose (\(C_{6}H_{12}O_{6}\)) is \(6 \times 12.01 + 12 \times 1.01 + 6 \times 16.00 = 180.18\) g/mol.<br /><br />The molecular weight of ethanol (\(C_{2}H_{5}OH\)) is \(2 \times 12.01 + 6 \times 1.01 + 16.00 + 1.01 = 46.07\) g/mol.<br /><br />Since the balanced equation shows that 2 molecules of ethanol are produced from one molecule of glucose, the total molecular weight of the desired product is \(2 \times 46.07 = 92.14\) g/mol.<br /><br />Substituting these values into the atom economy formula, we get:<br /><br />### \(Atom \, Economy = \frac{92.14}{180.18} \times 100\% = 51.13\%\)
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