To find the grams of ethanol [tex]\((C_2H_6O)\)[/tex] produced from 0.60 moles of glucose [tex]\((C_6H_{12}O_6)\)[/tex] during fermentation, we will follow the steps below:
1. Understand the Chemical Equation:
The balanced chemical equation for fermentation is:
[tex]\[
C_6H_{12}O_6(aq) \rightarrow 2C_2H_6O(aq) + 2CO_2(g)
\][/tex]
From the equation, we see that 1 mole of glucose produces 2 moles of ethanol.
2. Calculate Moles of Ethanol Produced:
Given that we have 0.60 moles of glucose, we can calculate the moles of ethanol formed:
[tex]\[
\text{Moles of ethanol} = 2 \times \text{Moles of glucose}
\][/tex]
Substituting the given moles of glucose:
[tex]\[
\text{Moles of ethanol} = 2 \times 0.60 = 1.2 \text{ moles}
\][/tex]
3. Determine Molar Mass of Ethanol:
The molar mass of ethanol [tex]\((C_2H_6O)\)[/tex] is calculated as follows:
- Carbon (C): [tex]\(12 \, \text{g/mol} \times 2 = 24 \, \text{g/mol}\)[/tex]
- Hydrogen (H): [tex]\(1 \, \text{g/mol} \times 6 = 6 \, \text{g/mol}\)[/tex]
- Oxygen (O): [tex]\(16 \, \text{g/mol} \times 1 = 16 \, \text{g/mol}\)[/tex]
Adding these together gives:
[tex]\[
\text{Molar mass of ethanol} = 24 + 6 + 16 = 46 \, \text{g/mol}
\][/tex]
4. Calculate the Mass of Ethanol Produced:
Using the moles of ethanol and its molar mass, we find the mass:
[tex]\[
\text{Mass of ethanol} = \text{Moles of ethanol} \times \text{Molar mass of ethanol}
\][/tex]
Substituting the values:
[tex]\[
\text{Mass of ethanol} = 1.2 \text{ moles} \times 46 \, \text{g/mol} = 55.2 \, \text{g}
\][/tex]
5. Round to Two Significant Figures:
The mass of ethanol, when rounded to two significant figures, is:
[tex]\[
55.2 \, \text{g}
\][/tex]
So, from 0.60 moles of glucose, 55.2 grams of ethanol are formed.
