Question 6.16: Diluting a Solution How would you prepare 500.0 mL of 0.2500......
Diluting a Solution
How would you prepare 500.0 mL of 0.2500 M NaOH solution starting from a concentration of 1.000 M?
STRATEGY
The problem gives initial and final concentrations (M_i and M_f) and final volume (V_f) and asks for the initial volume (V_i) that we need to dilute. Rewriting the equation M_i \times V_i = M_f \times V_f as V_i = (M_f/M_i) \times V_f gives the answer
V_{\mathrm{i}}=\frac{\mathrm{M}_{\mathrm{f}}}{\mathrm{M}_{\mathrm{i}}} \times V_{\mathrm{f}}=\frac{0.2500 \ \cancel{M}}{1.000 \ \cancel{M}} \times 500.0 \mathrm{~mL}=125.0 \mathrm{~mL}
We need to place 125.0 mL of 1.000 M NaOH solution in a 500.0 mL volumetric flask and fill to the calibration mark with water.
BALLPARK CHECK
Because the concentration decreases by a factor of four after dilution (from 1.000 M to 0.2500 M), the volume must increase by a factor of four. Thus, to prepare 500.0 mL of solution, we should start with 500.0/4 = 125.0 mL.