A chemist prepares a solution by mixing water and alcohol in a ratio by volume (water : alcohol). How many milliliters of alcohol are required to make liters of the solution?
For ratio mixture problems, first convert the ratio into a fraction of the total (add the parts and put the desired part over that sum). Make sure all quantities are in the units asked for in the question (here, convert liters to milliliters). Then multiply the total amount by the fraction corresponding to the component you are solving for, and double-check that you used the correct part of the ratio (alcohol vs. water).
Hints
Use the ratio to find the fraction for alcohol
The ratio of water to alcohol is . How many total parts are there, and what fraction of those parts is alcohol?
Work with milliliters, not liters
The final answer must be in milliliters. Convert liters to milliliters before you use the fraction from the ratio.
Apply the fraction to the total volume
Once you know the total volume in milliliters and the fraction that is alcohol, multiply the total volume by that fraction to find the milliliters of alcohol.
Desmos Guide
Compute the alcohol volume directly
In Desmos, type (3/10)*5.6*1000 and press Enter. The output is the number of milliliters of alcohol needed for the solution.
Step-by-step Explanation
Find the fraction of the solution that is alcohol
The ratio of water to alcohol is .
Add the parts to find the total number of parts:
- Total parts .
So alcohol makes up out of equal parts of the solution, which is the fraction of the total volume.
Convert the total solution volume to milliliters
The total volume of the solution is liters.
Use the conversion liter milliliters:
So the total solution volume is milliliters.
Calculate the volume of alcohol
Alcohol is of the total milliliters.
Compute:
So, the chemist needs 1680 milliliters of alcohol.