Prepare 100 ml of 1:100 bleach solution from a 1:10 bleach solution
a. How much volume of bleach solution will you need?
b. How much volume of water is needed?
c. Determine the percentage of chlorine concentration from the solution
The correct answer and explanation is :
To prepare 100 mL of a 1:100 bleach solution from a 1:10 bleach solution, we’ll use the concept of dilution. The formula for dilution is:
[
C_1V_1 = C_2V_2
]
Where:
- (C_1) is the concentration of the initial solution (1:10 bleach solution).
- (V_1) is the volume of the initial solution we need to use.
- (C_2) is the concentration of the final solution (1:100 bleach solution).
- (V_2) is the volume of the final solution (100 mL in this case).
Step-by-Step Solution
a. How much volume of bleach solution will you need?
We are given the following:
- (C_1 = \frac{1}{10}) (1:10 bleach solution)
- (C_2 = \frac{1}{100}) (1:100 bleach solution)
- (V_2 = 100 \, \text{mL})
We need to find (V_1), the volume of the 1:10 bleach solution needed.
Using the dilution formula:
[
C_1V_1 = C_2V_2
]
Substitute the known values:
[
\left(\frac{1}{10}\right) V_1 = \left(\frac{1}{100}\right) \times 100
]
Simplifying:
[
\frac{V_1}{10} = 1
]
Solving for (V_1):
[
V_1 = 10 \, \text{mL}
]
So, you will need 10 mL of the 1:10 bleach solution.
b. How much volume of water is needed?
The final volume required is 100 mL, and we need to subtract the 10 mL of the 1:10 bleach solution used. Thus, the volume of water needed is:
[
\text{Volume of water} = V_2 – V_1 = 100 \, \text{mL} – 10 \, \text{mL} = 90 \, \text{mL}
]
So, you will need 90 mL of water.
c. Determining the percentage of chlorine concentration in the solution
Now, let’s determine the chlorine concentration in the final solution.
- The concentration of the original 1:10 bleach solution is 10%, which means that in every 100 mL of solution, 10 mL is bleach (chlorine).
- When we dilute the 1:10 solution by mixing 10 mL of it with 90 mL of water, the concentration will decrease proportionally.
The final concentration is:
[
\text{Final concentration} = \frac{\text{Chlorine in the final solution}}{\text{Total volume}} \times 100
]
The chlorine in the final solution comes from 10 mL of the 1:10 bleach solution, which contains 10% chlorine. Therefore:
[
\text{Chlorine amount} = 10 \, \text{mL} \times 10\% = 1 \, \text{mL} \, \text{of chlorine}
]
The total volume of the final solution is 100 mL. Thus, the percentage of chlorine is:
[
\text{Percentage of chlorine} = \frac{1 \, \text{mL}}{100 \, \text{mL}} \times 100 = 1\%
]
Final Answer:
- a. You will need 10 mL of the 1:10 bleach solution.
- b. You will need 90 mL of water.
- c. The percentage of chlorine concentration in the final 1:100 solution is 1%.
Explanation:
The dilution process essentially reduces the concentration of bleach by adding water. Starting with a concentrated 1:10 bleach solution, which is 10% chlorine, we calculate the amount needed to dilute it to a much less concentrated solution, 1:100, which corresponds to a 1% chlorine concentration. Using the dilution formula ensures the correct amount of each component is used to achieve the desired final concentration.