# Question #80d6a

##### 1 Answer

#### Explanation:

The first thing to do here is make sure that the two volumes given to you are expressed using the **same units**.

You can convert *microliters*, *milliliters*,

#color(purple)(|bar(ul(color(white)(a/a)color(black)("1 mL" = 10^3mu"L")color(white)(a/a)|)))#

In your case, the sample of urine will have a volume equivalent to

#50 color(red)(cancel(color(black)(mu"L"))) * "1 mL"/(10^3color(red)(cancel(color(black)(mu"L")))) = "0.050 mL"#

Now, the **dilution factor** is calculated by dividing the **final volume** of the solution, which is the volume of the *diluted solution*, by the **initial volume** of the solution, which is the volume of the *concentrated* solution.

#color(blue)(|bar(ul(color(white)(a/a)"DF" = V_"diluted"/V_"concentrated" color(white)(a/a)|)))#

The volume of the **diluted solution** is equal to the volume of the concentrated sample, which in this case is urine, plus the volume of the diluent, which in this case is water

#V_"diluted" = V_"concentrated" + V_"diluent"#

#V_"diluted" = "0.050 mL" + "0.150 mL" = "0.200 mL"#

The dilution factor will thus be equal to

#"DF" = (0.200 color(red)(cancel(color(black)("mL"))))/(0.050color(red)(cancel(color(black)("mL")))) = color(blue)(4)#

This tells you that the concentrated solution was **times more concentrated** than the diluted solution.