Question #6a10d

The underlying principle of a dilution is that the number of moles of solute remains unchanged.

In this regard, a dilution reduces the concentration of a solution by increasing its volume while keeping the number of moles of solute constant.

In this case, sample #"B"# is said to be a #1:10# dilution of sample #"A"#. This means that the concentration of sample #"B"# is #10# times lower than the concentration of sample #"A"# because the volume of sample #"B"# is #10# times higher than the volume of sample #"A"#.

So, let's say that sample #"A"# has a concentration #c_"A"# and a volume #V_"A"#.

To get sample #"B"#, you must add enough solvent to make the volume of sample #"B"# equal to

#V_"B" = 10 * V_"A"" " " "color(orange)("(*)")#

If you start with the initial volume of sample #"A"#, then you must add a volume of #9V_"A"# of solvent to make solution #"B"#.

Since the number of moles of solute is constant, you will have

#c_"A" = n/V_"A" -># for sample #"A"#

#c_"B" = n/V_"B" -># for sample #"B"#

But you know that you can use #color(orange)("(*)")# to write

#c_"B" = n/(10 * V_"A")#

Since #n# is equal to

#n = c_"A" * V_"A"#

you will get that

#c_"B" = (c_"A" * color(red)(cancel(color(black)(V_"A"))))/(10 * color(red)(cancel(color(black)(V_"A")))) = c_"A" / 10#

Therefore, you can say that the concentration of solution #"B"# is #10# times lower than the concentration of solution #"A"#.