To solve this problem, we'll use the dilution formula, which relates the concentration and volume of the original solution to the concentration and volume of the final diluted solution. The formula is:
[tex]\[ C1 \times V1 = C2 \times V2 \][/tex]
where:
- [tex]\( C1 \)[/tex] is the concentration of the stock solution.
- [tex]\( V1 \)[/tex] is the volume of the stock solution.
- [tex]\( C2 \)[/tex] is the concentration of the diluted solution.
- [tex]\( V2 \)[/tex] is the volume of the diluted solution, which we need to find.
Here are the given values from your problem:
- [tex]\( C1 = 10 \)[/tex] M (stock solution concentration)
- [tex]\( V1 = 50 \)[/tex] mL (volume of stock solution)
- [tex]\( C2 = 2 \)[/tex] M (desired concentration of diluted solution)
Now, we want to find [tex]\( V2 \)[/tex], so we rearrange the formula above to solve for [tex]\( V2 \)[/tex]:
[tex]\[ V2 = \frac{C1 \times V1}{C2} \][/tex]
Substitute the known values into the equation:
[tex]\[ V2 = \frac{10 \text{ M} \times 50 \text{ mL}}{2 \text{ M}} \][/tex]
Now carry out the calculations:
[tex]\[ V2 = \frac{500}{2} \][/tex]
[tex]\[ V2 = 250 \text{ mL} \][/tex]
The volume of the diluted solution [tex]\( V2 \)[/tex] is 250 mL. Therefore, when you dilute 50 mL of a 10 M stock solution to a concentration of 2 M, you can make a total volume of 250 mL of the diluted solution.
