Answer : The original volume of the ethanol is 37.5 mL
Explanation :
The balance chemical reaction will be,
![C2H_5OH+3O_2\rightarrow 2CO_2+3H_2O](https://img.qammunity.org/2019/formulas/chemistry/high-school/yuet6s07c211e6ekg8hauqydyg1pgo7xc0.png)
First we have to calculate the moles of
.
![\text{ Moles of }H_2O=\frac{\text{ Mass of }H_2O}{\text{ Molar mass of }H_2O}=(34.8)/(18g/mole)=1.93moles](https://img.qammunity.org/2019/formulas/chemistry/high-school/si6y5aumhk9vp8gjh4t1dl7o197dpyyvqt.png)
Now we have to calculate the moles of ethanol.
From the balanced reaction we conclude that,
As, 3 moles of
produce from 1 mole of ethanol
So, 1.93 moles of
produce from
mole of ethanol
Now we have to calculate the mass of ethanol.
![\text{ Mass of ethanol}=\text{ Moles of ethanol}* \text{ Molar mass of ethanol}](https://img.qammunity.org/2019/formulas/chemistry/high-school/7jkayn79ef0xefrd1ns3gtkpbc1wkkalds.png)
![\text{ Mass of ethanol}=(0.643moles)* (46g/mole)=29.6g](https://img.qammunity.org/2019/formulas/chemistry/high-school/g3xn2q6ly7jf95keq6v80dpsziz2oa4i3b.png)
Now we have to calculate the volume of ethanol.
![Density=(Mass)/(Volume)](https://img.qammunity.org/2019/formulas/chemistry/high-school/9d5g9m70r7bn2fve9o5ademps95pw8dj6o.png)
![0.789g/mL=(29.6g)/(Volume)](https://img.qammunity.org/2019/formulas/chemistry/high-school/rgiyja5q5e9i9102h2qh42ou9xa6vk47r5.png)
![Volume=(29.6g)/(0.789g/mL)=37.5mL](https://img.qammunity.org/2019/formulas/chemistry/high-school/r9kwvf06a0eppk2wa63uami4g0t85skstp.png)
Therefore, the original volume of the ethanol is 37.5 mL