What would be the concentration of a solution made by adding 250 mL of water to 45.0 mL of 4.2 M KOH?

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Answer 1 · 2014-05-18T21:44:36

The concentration of the solution would be 0.64 mol/L.

Method 1

One way to calculate the concentration of a diluted solution is to use the formula

#c_1V_1 = c_2V_2#

#c_1# = 4.2 mol/L; #V_1# = 45.0 mL = 0.0450 L
#c_2# = ?; #V_2# = (250 + 45.0) mL = 295 mL = 0.295 L

Solve the formula for #c_2#.

# c_2 = c_1 × V_1/V_2# = 4.2 mol/L × #(45.0" mL")/(295" mL")# = 0.64 mol/L

Method 2

Remember that the number of moles is constant

#n_1 = n_2#

#n_1 = c_1V_1# = 4.2 mol/L × 0.0450 L = 0.19 mol

#n_2 = c_2V_2 = n_1# = 0.19 mol

#c_2 = n_2/V_2 = (0.19" mol")/(0.295" L")# = 0.64 mol/L

This makes sense. You are increasing the volume by a factor of about 7. So the concentration should decrease by a factor of about 7.

#4.2/7# = 0.6