Question 9.15: A doctor orders 1000. mL of a 35.0% (m/v) dextrose solution....
A doctor orders 1000. mL of a 35.0% (m/v) dextrose solution. If you have a 50.0% (m/v) dextrose solution, how many milliliters would you use to prepare 1000. mL of 35.0% (m/v) dextrose solution?
STEP 1 Prepare a table of the concentrations and volumes of the solutions.
| ANALYZE THE PROBLEM | Given | Need | Connect |
| C_{1} = 50% (m/v)
C_{2} = 35.0% (m/v) V_{2} = 1000. mL |
\boxed{V_{1}} | C_{1}V_{1} = C_{2}V_{2}
Predict: C_{1} increases, |
STEP 2 Rearrange the dilution expression to solve for the unknown quantity.
C_{1} \boxed{V_{1}}= C_{2}V_{2}
\frac{\cancel{C_{1}}\boxed{V_{1}}}{\cancel{C_{1}}} = \frac{\boxed{C_{2}}V_{2}}{C_{1}} Divide both sides by C_{1}
\boxed{V_{1}}= V_{2} \times \frac{C_{2}}{C_{1}}STEP 3 Substitute the known quantities into the dilution expression and calculate.
\boxed{V_{1}} =\underset{Four SFs}{1000 mL} \times \overset{Three SFs}{\underset{decreases volume }{\underset{Concentration fatcor }{\underset{Three SFs}{\frac{35.0 \cancel{\%}}{50.0 \cancel{\%}}} } }} = \underset{Three SFs}{700. mL of dextrose solution }When the final volume (V_{2}) is multiplied by a ratio of the percent concentrations (concentration factor) that is less than 1, the initial volume (V_{1}) is less than the final volume (V_{2}) as predicted in Step 1. .