Figuring out the amount of water to add to alcohol in order to achieve a desired alcohol percentage can be useful for many applications. In chemistry, pharmacology, cooking, and making beverages like cocktails or wine, obtaining a solution with an exact alcohol percentage is often necessary.
In this article, we will walk through the step-by-step calculations needed to determine how much water to add to 48 ml of alcohol in order to end up with a 25% alcohol solution. We will look at the concepts involved, go through examples, and provide a detailed explanation of the math required at each step along the way.
Basic Concepts
Before jumping into the specific example of adding water to 48 ml of alcohol, let’s review some of the basic concepts and formulas that are needed to solve these types of dilution problems.
Volume Percent Concentration
Percentage concentration by volume, often shortened to volume percent or % v/v, is used to express the concentration of a solute in a solution when mixing liquids. It is defined as:
Volume percent = (Volume of solute / Total volume of solution) x 100%
For example, to make a 25% v/v solution, 25% of the total volume is taken up by the solute or alcohol, while the remaining 75% of the volume is the solvent or water. The % v/v allows us to calculate the volume of solute and solvent required to achieve a desired concentration percentage.
Dilution Equation
To calculate how to dilute a solution to a lower concentration, the dilution equation is used:
C1V1 = C2V2
Where:
- C1 = Initial concentration
- V1 = Initial volume
- C2 = Final concentration
- V2 = Final volume
By rearranging the dilution equation to solve for the variable needed, we can determine the amount of solvent (water) that must be added to dilute a solution to a specified lower concentration.
Step-by-Step Calculations
Now that we have reviewed the main concepts and formulas, let’s go through the detailed calculations required for this specific example question:
How many ml of water must be added to 48 ml of alcohol to make a solution that contains 25% of alcohol?
Let’s go through this step-by-step:
- Define the known variables from the question:
- Initial volume (V1) = 48 ml
- Initial concentration (C1) = 100% (pure alcohol)
- Final concentration (C2) = 25%
- Set up the dilution equation, substituting in the known values:
- C1V1 = C2V2
- (100%)(48 ml) = (25%)(V2)
- Solve the dilution equation for the unknown final volume (V2):
- 100% x 48 ml = 25% x V2
- 4800 = 0.25V2
- V2 = 4800/0.25
- V2 = 19,200 ml
- The final volume required is 19,200 ml
- To calculate the amount of water to be added:
- Total final volume = V2 = 19,200 ml
- Initial alcohol volume = 48 ml
- Therefore, the water volume to be added = Total volume – Initial alcohol volume
- Water to be added = 19,200 ml – 48 ml = 19,152 ml
- Rounding to the nearest whole number, 19,152 ml of water must be added to 48 ml of alcohol to create a 25% alcohol solution.
Examples
Let’s look at a couple more examples to solidify understanding of these dilution calculations:
Example 1
If you have 325 ml of an 80% alcohol solution, how much water would you need to add to dilute it to a 40% solution?
- C1 = 80% = 0.80
- V1 = 325 ml
- C2 = 40% = 0.40
- Use dilution equation: (0.80)(325 ml) = (0.40)(V2)
- 260 = 0.40V2
- V2 = 650 ml
- Water to add = Total volume – Initial volume
= 650 ml – 325 ml = 325 ml
For this example, you would need to add 325 ml of water to the 80% alcohol solution to create a 40% solution.
Example 2
A chemistry experiment requires 150 ml of a 15% saline solution. If you have a 45% saline stock solution, how much of it would you need to dilute down to 150 ml of a 15% solution?
- C1 = 45% = 0.45
- V1 = ? (unknown initial volume)
- C2 = 15% = 0.15
- V2 = 150 ml
- Use dilution equation: (0.45)(V1) = (0.15)(150 ml)
- 0.45V1 = 22.5
- V1 = 50 ml
For this example, you would need 50 ml of the 45% stock solution diluted with additional water to reach a total volume of 150 ml to achieve a 15% saline solution.
Why Dilution Calculations Are Important
Now that we’ve looked in detail at how to perform these dilution calculations, it’s worth discussing why these skills are so important for chemistry, biology, medicine, cooking, and other fields.
Some key reasons dilution calculations matter include:
- Achieving accurate concentrations of solutions is critical for experiments to work properly in chemistry, biology, and medicine. The wrong concentrations can alter results and ruin experimental accuracy.
- Calculating the correct dilutions allows the most economical use of often expensive chemical or biological reagents and solutions.
- Pharmacists and doctors must determine accurate dilutions when preparing intravenous (IV) medications to be administered to patients at specific dosages.
- Food scientists and chefs need to calculate dilutions when developing or adjusting recipes to engineered specific flavors, textures, or other properties.
- Beverage producers have to figure proper dilutions when making alcoholic or other drinks to achieve desired tastes and alcohol contents.
Mistakes in dilution calculations can lead to wasted materials, failed experiments, incorrect drug delivery, food safety issues, badly flavored beverages, and more. Mastering how to accurately calculate dilutions is a foundational skill for many scientific and cooking fields.
Tips for Dilution Calculations
Here are some useful tips to keep in mind when doing dilution calculations:
- Remember that percent solutions express concentration as a percentage by volume (v/v). 10% is 10 ml solute per 100 ml solution.
- The dilution equation relates the initial concentration and volume to the final desired concentration and volume. Know how to rearrange it to isolate the unknown variable.
- Double check your calculation setup and make sure variables are plugged into the dilution equation correctly.
- Use a calculator to avoid simple math errors when plugging values into the equation.
- Round your final volume answer to the nearest whole number; you can’t add fractional milliliters when diluting by hand.
- Always add solute to solvent when diluting; never add solvent to solute which can alter the final concentration.
- Carefully measure volumes when actually preparing the dilution to achieve the most accuracy.
Practice Dilution Problems
Practice is the best way to master dilution calculations. Here are some additional examples to work through on your own:
- You have 285 ml of a 65% ethanol solution. How much water would you need to add to make it a 10% ethanol solution?
- If you need 200 ml of a 20% bleach cleaning solution, how much of a concentrated 36% bleach solution would be required?
- For a chemistry experiment, you need 250 ml of a 2.5M acid solution. How much of a 5.0M acid stock solution would you have to dilute down?
- A recipe calls for 100 ml of 80 proof (40%) vodka sauce. How much 100 proof (50%) vodka would you need to add?
- How much water is needed to dilute 75 ml of pure lemon juice concentrate down to 250 ml of a 20% lemon juice solution?
Take your time to walk through the multiple steps for each practice problem. Check your work, and then compare your answers to the solutions below:
Practice Problem Solutions
-
C1 = 65% = 0.65
V1 = 285 ml
C2 = 10% = 0.10
(0.65)(285 ml) = (0.10)(V2)
185.25 = 0.10V2
V2 = 1,852.5 ml
Water to add = 1,852.5 ml – 285 ml = 1,567.5 ml
Add 1,568 ml water
-
C1 = 36% = 0.36
V1 = ?
C2 = 20% = 0.20
V2 = 200 ml
(0.36)(V1) = (0.20)(200 ml)
0.36V1 = 40
V1 = 111 ml
Use 111 ml of 36% bleach solution
-
C1 = 5.0 M
V1 = ?
C2 = 2.5 M
V2 = 250 ml
(5.0 M)(V1) = (2.5 M)(250 ml)
5.0V1 = 625
V1 = 125 ml
Dilute 125 ml of 5.0 M solution
-
C1 = 50% = 0.50
V1 = ?
C2 = 40% = 0.40
V2 = 100 ml
(0.50)(V1) = (0.40)(100 ml)
0.50V1 = 40
V1 = 80 ml
Use 80 ml of 50% vodka
-
C1 = 100%
V1 = 75 ml
C2 = 20% = 0.20
V2 = 250 ml
(100%)(75 ml) = (0.20)(250 ml)
7500 = 50
V2 = 175 ml
Water to add = V2 – V1 = 175 ml – 75 ml = 100 ml
Add 100 ml water
With practice, these multistep dilution calculations will become second nature. Always take it step-by-step and double check your work. Having mastery of these important skills will serve you well in any science or cooking discipline.
Conclusion
In summary, here are some key points to remember about dilution calculations:
- Use percent solutions by volume to express solute concentration
- Rearranged the dilution equation C1V1 = C2V2 to isolate the unknown
- Add solute to solvent carefully when preparing dilutions
- Take your time and walk through the calculations methodically
- Practice sample problems to gain experience and mastery
- Accurate dilutions are critical for experiments, medicine, food, and beverages
Following the steps outlined here for calculating the proper dilutions will give you the knowledge and skills for success in any field where precise concentrations are important. With diligence and practice, you’ll be diluting solutions like a pro in no time!
