# If 250g of sugar is completely fermented to ethanol, what is the theoretical yield of ethyl alcohol in: ?

##
i. grams or milliliters (density of ethanol is 0.79g/mL)

ii. what is the final %v/v of alcohol if that 250 sugar was used to make 1L of wine? (assume no volume changed during fermentation)

please, show me the working out.

Thanks

i. grams or milliliters (density of ethanol is 0.79g/mL)

ii. what is the final %v/v of alcohol if that 250 sugar was used to make 1L of wine? (assume no volume changed during fermentation)

please, show me the working out.

Thanks

##### 2 Answers

Here's what I got.

#### Explanation:

Start by writing the chemical equation that describes this reaction

#"C"_ 6"H"_ 12"O"_ (6(aq)) -> 2"C"_ 2"H"_ 5"OH"_ ((aq)) + 2"CO"_ (2(g)) uarr#

**SIDE NOTE** *As you can see, I am assuming that by* *of sugar you mean* *of glucose, not sucrose,*

*If you were supposed to work with sucrose instead of glucose, add this step*

#"C"_ 12"H"_ 22"O"_ (11(aq)) + "H"_ 2"O"_ ((l)) -> 2"C"_ 6"H"_ 12 "O"_ (6(aq))#

*and redo the calculations with the mass of glucose that you'll get from this reaction.*

Now, notice that you have a **mole ratio** between glucose and ethanol, so convert the mass of glucose to *moles* by using the compound's **molar mass**

#250 color(red)(cancel(color(black)("g"))) * "1 mole glucose"/(180.156color(red)(cancel(color(black)("g")))) = "1.388 moles glucose"#

This means that the reaction will produce

#1.388 color(red)(cancel(color(black)("moles glucose"))) * "2 moles ethanol"/(1color(red)(cancel(color(black)("mole glucose")))) = "2.776 moles ethanol"#

To convert this to *grams*, use the **molar mass** of ethanol

#2.776 color(red)(cancel(color(black)("moles ethanol"))) * "46.07 g"/(1color(red)(cancel(color(black)("mole ethanol")))) = "127.9 g"#

Rounded to two **sig figs**, the answer will be

#color(darkgreen)(ul(color(black)("theoretical yield = 130 g")))#

To convert this to *milliliters*, use the **density** of ethanol

#127.9 color(red)(cancel(color(black)("g"))) * "1 mL"/(0.79color(red)(cancel(color(black)("g")))) = color(darkgreen)(ul(color(black)("160 mL")))#

To find the *volume by volume percent concentration* of the wine, **volume** of ethanol produced by the reaction in a total volume of

Now, the solution's volume by volume percent concentration tells you the volume of solute present for every

In your case,

#100 color(red)(cancel(color(black)("mL solution"))) * "160 mL ethanol"/(10^3color(red)(cancel(color(black)("mL solution")))) = "16 mL ethanol"#

Therefore, the concentration by volume will be

#color(darkgreen)(ul(color(black)("% v/v = 16% ethanol")))#

I'll leave the answer rounded to two **sig figs**, but don't forget that you only have one significant figure for the volume of wine.

i. The theoretical yield of ethanol is 135 g or 170 mL; ii.the final concentration is 17 % v/v.

#### Explanation:

We know that we will need a balanced equation with masses and moles, so let's gather all the information in one place.

I assume that by "sugar" you mean sucrose,

**Step 1. Calculate the moles of sugar**

**Step 2. Calculate the moles of ethanol**

**Step 3. Calculate the mass of ethanol**

**Step 4. Calculate the volume of ethanol**

**Step 5. Calculate the volume % of ethanol**