How do you do dilution calculations?

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Answer 1 · 2014-06-17T23:27:37

You use the formula #V_1c_1 = V_2c_2#.

In any dilution, the number of moles of solute stays the same. You are simply increasing the amount of solvent in the solution.

You know that

Moles = #"litres" × "moles"/"litres"# = volume × molarity = #V× c#.

So, if moles before dilution = moles after dilution,

#V_1c_1 = V_2c_2#.

Example 1. Calculating new concentration

A chemist starts with 50.0 mL of a 0.400 mol/L NaCl solution and dilutes it to 1000. mL. What is the concentration of NaCl in the new solution?

Solution 1

#V_1c_1 = V_2c_2#

#V_1# = 50.0 mL; #c_1# = 0.400 mol/L
#V_2# = 1000. mL; #c_2# = ?

#c_2 = c_1 × V_1/V_2# = 0.400 mol/L × #(50.0"mL")/(1000"mL")# = 0.0200 mol/L

Note: You don't have to convert the volumes to litres, but you must use the same units on each side of the equation.

Example 2. Calculating initial volume

A chemist wants to make 500. mL of 0.0500 mol/L HCl by diluting a 6.00 mol/L HCl solution. How much of that solution should she use?

Solution 2

#V_1# = 500. mL; #c_1# = 0.0500 mol/L
#V_2# = ?; #c_2# = 6.00 mol/L

#V_2 = V_1 × c_1/c_2# = 500. mL × #(0.0500"mol/L")/(6.00"mol/L")# = 4.17 mL

Hope this helps.