Question 9.13: Aqueous NaOH can be purchased at a concentration of 1.0 M. H...
Aqueous NaOH can be purchased at a concentration of 1.0 M. How would you use this concentrated solution to prepare 750 mL of 0.32 M NaOH?
ANALYSIS The number of moles of solute is constant, so
Of the four variables in this equation, we know the initial concentration M_1 (1.0 M), the final volume V_2 (750 mL), and the final concentration M_2 (0.32 M), and we need to find the initial volume V_1.
BALLPARK ESTIMATE We want the solution concentration to decrease by a factor of about 3, from 1.0 M to 0.32 M, which means we need to dilute the 1.0 M solution by a factor of 3. This means the final volume must be about 3 times greater than the initial volume. Because our final volume is to be 750 mL, we must start with an initial volume of about 250 mL.
Solving the above equation for V_1 and substituting in the known values gives
V_1 = \frac{V_2M_2}{M_2} = \frac{(750 mL)(0.32 \cancel{M})}{1.0 \cancel{M}} = 240 mLTo prepare the desired solution, dilute 240 mL of 1.0 M NaOH with water to make a final volume of 750 mL.
BALLPARK CHECK: The calculated answer (240 mL) is reasonably close to our estimate of 250 mL.