Chemistry dilution question?

What volume of water needs to be added to 25ml of 0·2mol/l calcium chloride solution to produce a solution with a chloride ion concentration of 0·1mol/l?

A 25ml
B 50ml
C 75ml
D 100ml

1 Answer
Apr 18, 2018

#"C."#

Explanation:

For dilutions, we use the formula:

#V_1c_1=V_2c_2#

  • #V_1,V_2# are the volumes of the two solutions

  • #c_1,c_2# are the concentrations of the two solutions

Since the original concentration of calcium chloride has a concentration of #2 \ "mol/L"=2 \ "M"#, and the new concentration wants us to have a CHLORIDE ION CONCENTRATION OF #0.1 \ "mol/L"#, we need to be careful here.

Calcium chloride has a chemical formula of #CaCl_2#. So, in one mole per liter of this solution, there exist TWO moles per liter of chloride ions. So, if we want to have a #0.1 \ "M"# concentration of chloride ions, we need to use a #(0.1 \ "M")/2=0.05 \ "M"# calcium chloride solution.

And so, we got:

#25 \ "mL"*0.2 \ "M"=v_2*0.05 \ "M"#

#v_2=(25 \ "mL"*0.2color(red)cancelcolor(black)"M")/(0.05color(red)cancelcolor(black)"M")#

#=100 \ "mL"#

So, the new solution would have a volume of #100 \ "mL"#. But since the starting volume was #25 \ "mL"#, we must add a total of:

#100 \ "mL"-25 \ "mL"=75 \ "mL"# of water

Therefore, #"C."# is the correct answer.