Distilled solution content of ethanol varies between 4.7 - 39.5 vol-%. If content of ethanol is  15.8 vol-% and distilled ethanol content is a 100 vol-% ethanol volume is 115 liters, what is the original distilled solution total volume

We are given that the ethanol content in the original distilled solution is 15.8 vol-%, and that when the ethanol is distilled out, the volume of pure ethanol is 115 liters.

Let's denote:
- \( V_{original} \) as the total volume of the original distilled solution (which we need to find).
- \( c_{ethanol} \) as the ethanol content in the original solution, which is 15.8 vol-% or 0.158 as a decimal.
- The volume of pure ethanol distilled, \( V_{ethanol} = 115 \) liters.

Now, the relationship between the ethanol content and the volume of the original solution is given by:

\[
c_{ethanol} \times V_{original} = V_{ethanol}
\]

Substituting the known values:

\[
0.158 \times V_{original} = 115
\]

Solving for \( V_{original} \):

\[
V_{original} = \frac{115}{0.158} \approx 727.85 \, \text{liters}
\]

Thus, the total volume of the original distilled solution is approximately **727.85 liters**.

Would you like further details on this or have any questions? 

Here are 5 related questions to explore:
1. How does ethanol content affect the distillation process efficiency?
2. What happens to the volume of ethanol during fractional distillation?
3. How do we calculate ethanol content in a mixture after multiple distillations?
4. What is the relationship between vol-% and mass-% in ethanol-water solutions?
5. How does temperature influence ethanol concentration in distillation?

**Tip:** When converting percentages to decimals, divide by 100 to ensure proper calculations.

Distilled solution content of ethanol varies between 4.7 - 39.5 vol-%. If content of ethanol is 15.8 vol-% and distilled ethanol content is a 100 vol-% ethanol volume is 115 liters, what is the original distilled solution total volume?

Solve the problem of finding the original volume of an ethanol solution given a 15.8 vol-% ethanol content and a distilled ethanol volume of 115 liters. Learn key concepts like volume calculation and percentages, suitable for Grades 10-12.

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