# Question #e7667

##### 1 Answer

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.

#color(blue)("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

#"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 **50**.