# Question e7667

Aug 17, 2015

The dilution factor is 50.

#### Explanation:

The dilution factor is simply thwe ratio between the final volume of the solution and the nitial volume of the sample.

$\textcolor{b l u e}{\text{DF" = V_"final"/V_"initial}}$

In your case, you have 0.5 g of a solute that is disolved in 100 mL of solution.

Now comes the interesting part. Out of this solution, you take a 10-mL sample which you then dilute to a final volume of 500 mL.

The initial volume of the sample is 10 mL, the final volume of the solution is 500 mL, which means that the dilution factor is

$\text{DF" = V_"final"/V_"initial}$

"DF" = (500color(red)(cancel(color(black)("mL"))))/(10color(red)(cancel(color(black)("mL")))) = color(green)(50)

Now, don't get confused about the volume of the stock solution. When you dissolve 0.5 g of solute in 100 mL of water, you're not diluting anything, you're just making a solution.

The 10-mL sample of this solution would contain

10color(red)(cancel(color(black)("mL"))) * "0.5 g solute"/(100color(red)(cancel(color(black)("mL")))) = "0.05 g solute"#

The final solution will contain the same amount of solute as the 10-mL sample, but the volume will now be 50 times greater. This means that you have the same amount of solute in 50 times the volume of solution $\to$ you diluted the solution by a factor of 50.