Answer
See answer below.
Work Step by Step
Titration 1:
Number of moles of $AgNO_3$:
$41.00\ mL\times 0.0750\ M=3.075\ mmol$, same as the chloride ion.
Concentration: $3.075\ mmol/50.0\ mL=0.0615\ M$
Original solution: $0.0615\ M\times 0.250\ L=0.0154\ mol$
Mass of KCl: $0.0154\ mol\times 74.55\ g/mol=1.15\ g$
Mass percentage: $1.15/4.00\times100\%=28.7\%$
Titration 2:
Number of moles of $AgNO_3$:
$38.12\ mL\times 0.0750\ M=2.860\ mmol$, same as chloride
From the first titration, number of moles of chlorides from perchlorate:
$2.860\ mmol-0.0615\ M\times 25.00\ mL=1.322\ mmol$
Concentration: $1.322\ mmol/25.0\ mL=0.0529\ M$
Original solution: $0.0529\ M\times 0.250\ L=0.0154\ mol$
Mass of $KClO_4$: $0.0132\ mol\times 138.54\ g/mol=1.83\ g$
Mass percentage: $1.83/4.00\times100\%=45.7\%$
