What is the percentage strength (v/v) of Diluted Alcohol, NF, which results from mixing 50 mL of Alcohol, USP (95.0%, v/v) with 50 mL of Purified Water, USP?
C1xV1 = C2xV2
95% x 50ml = C2 x 97ml
C2 = 49%
This was an example my professor put up. I can not comprehend why 97 ml is used as V2. Is it not 100ml when you are mixing 50ml of a solution with 50ml of water?
Nvm. Apparently when you mix water and alcohol theres a contraction effect that reduces the final vol by ~3%.
I seem to remember that 50 mL water + 50 mL ethyl alcohol gives 95 mL solution.
The calculation you provided uses the equation C1 x V1 = C2 x V2, where C1 is the initial concentration, V1 is the initial volume, C2 is the final concentration, and V2 is the final volume.
In this example, you are trying to find the final concentration of the diluted alcohol solution. The initial volume, V1, is given as 50 mL of Alcohol, USP (95.0%, v/v), and the final volume, V2, is the total volume after mixing, which is unknown.
By substituting the given values into the equation, you have:
(95% x 50 mL) = (C2 x V2)
To solve for C2, you need to know the final volume, V2. In this case, it seems like your professor assumed the total volume would be 100 mL (50 mL of alcohol + 50 mL of water). However, the calculation you mentioned used 97 mL instead.
Without further information or clarification, it is unclear why your professor used 97 mL instead of 100 mL. It's possible they may have been accounting for a small loss of volume during the mixing process or using a more precise measurement. It would be best to ask your professor for clarification to ensure you have the correct information.
The formula C1V1 = C2V2 is used to calculate the concentration or strength of a solution after it has been diluted. In this case, C1 represents the initial concentration of the Alcohol, USP (95.0%, v/v), V1 represents the volume of the Alcohol, USP used (50 mL), C2 represents the final concentration or strength of the diluted solution, and V2 represents the total volume of the final diluted solution.
For this specific problem, you are mixing 50 mL of Alcohol, USP (95.0%, v/v) with 50 mL of Purified Water, USP. The total volume of the final diluted solution will indeed be 100 mL. However, we need to consider that we are not only diluting the alcohol but also adding the volume of the water. Therefore, V2 will be the total volume of the final diluted solution, which is 50 mL (from the alcohol) + 50 mL (from the water) = 100 mL.
By substituting the given values into the formula C1V1 = C2V2, we can calculate the final concentration or strength of the diluted solution:
(95.0%)(50 mL) = C2(100 mL)
Simplifying the equation:
4750 = 100C2
Dividing both sides of the equation by 100:
C2 ≈ 47.5%
Therefore, the percentage strength (v/v) of the Diluted Alcohol, NF, resulting from mixing 50 mL of Alcohol, USP (95.0%, v/v), with 50 mL of Purified Water, USP, is approximately 47.5%.