If 41.7 g of [tex]$KCl \, ( MM = 74.55 \, g/mol )$[/tex] are added to a 500.0 mL volumetric flask, and water is added to fill the flask, what is the concentration of [tex]$KCl$[/tex] in the resulting solution?
1. Identify the given data: - Mass of [tex]\( KCl \)[/tex] [tex]\( (m) \)[/tex]: 41.7 grams - Molar mass of [tex]\( KCl \)[/tex] [tex]\( (M) \)[/tex]: 74.55 grams per mole - Volume of the solution [tex]\( (V) \)[/tex]: 500.0 milliliters
2. Convert the volume from milliliters to liters: [tex]\[
V = \frac{500.0 \text{ mL}}{1000} = 0.5 \text{ L}
\][/tex]
3. Calculate the number of moles of [tex]\( KCl \)[/tex]: We use the formula for moles: [tex]\[
\text{moles of } KCl = \frac{\text{mass of } KCl}{\text{molar mass of } KCl}
\][/tex] Substituting the values: [tex]\[
\text{moles of } KCl = \frac{41.7 \text{ g}}{74.55 \text{ g/mol}} \approx 0.559356 \text{ moles}
\][/tex]
4. Calculate the concentration of the solution: The concentration [tex]\( C \)[/tex] in molarity is given by: [tex]\[
C = \frac{\text{moles of solute}}{\text{volume of solution in liters}}
\][/tex] Substituting the values: [tex]\[
C = \frac{0.559356 \text{ moles}}{0.5 \text{ L}} \approx 1.118712 \text{ mol/L}
\][/tex]
Therefore, the concentration of [tex]\( KCl \)[/tex] in the resulting solution is approximately [tex]\( 1.1187 \text{ mol/L} \)[/tex].
