Answer :
Sure, let's find the concentration of the saturated [tex]\( Ca(OH)_2 \)[/tex] solution step-by-step.
1. Understand the Reaction:
The balanced chemical reaction for titrating [tex]\( Ca(OH)_2 \)[/tex] with [tex]\( HCl \)[/tex] is:
[tex]\[ Ca(OH)_2 + 2HCl \rightarrow CaCl_2 + 2H_2O \][/tex]
This tells us that 1 mole of [tex]\( Ca(OH)_2 \)[/tex] reacts with 2 moles of [tex]\( HCl \)[/tex].
2. Determine Moles of [tex]\( HCl \)[/tex] Used:
You have 35.9 mL of 0.026 M [tex]\( HCl \)[/tex]. First, convert the volume from mL to L by dividing by 1000:
[tex]\[ 35.9 \, \text{mL} = 0.0359 \, \text{L} \][/tex]
Calculate the moles of [tex]\( HCl \)[/tex] using the formula:
[tex]\[ \text{moles of } HCl = \text{Molarity} \times \text{Volume (L)} \][/tex]
[tex]\[ \text{moles of } HCl = 0.026 \, \text{M} \times 0.0359 \, \text{L} = 0.0009334 \, \text{moles} \][/tex]
3. Relate Moles of [tex]\( HCl \)[/tex] to Moles of [tex]\( Ca(OH)_2 \)[/tex]:
According to the balanced equation, 2 moles of [tex]\( HCl \)[/tex] react with 1 mole of [tex]\( Ca(OH)_2 \)[/tex]. Therefore, divide the moles of [tex]\( HCl \)[/tex] by 2 to find moles of [tex]\( Ca(OH)_2 \)[/tex]:
[tex]\[ \text{moles of } Ca(OH)_2 = \frac{0.0009334}{2} = 0.0004667 \, \text{moles} \][/tex]
4. Calculate Concentration of [tex]\( Ca(OH)_2 \)[/tex]:
The volume of the [tex]\( Ca(OH)_2 \)[/tex] solution is 25.0 mL. Convert this to liters:
[tex]\[ 25.0 \, \text{mL} = 0.0250 \, \text{L} \][/tex]
Find the concentration using the formula:
[tex]\[ \text{Concentration (M)} = \frac{\text{moles}}{\text{Volume (L)}} \][/tex]
[tex]\[ \text{Concentration of } Ca(OH)_2 = \frac{0.0004667}{0.0250} = 0.018668 \, \text{M} \][/tex]
So, the concentration of the saturated [tex]\( Ca(OH)_2 \)[/tex] solution is approximately 0.01867 M.
1. Understand the Reaction:
The balanced chemical reaction for titrating [tex]\( Ca(OH)_2 \)[/tex] with [tex]\( HCl \)[/tex] is:
[tex]\[ Ca(OH)_2 + 2HCl \rightarrow CaCl_2 + 2H_2O \][/tex]
This tells us that 1 mole of [tex]\( Ca(OH)_2 \)[/tex] reacts with 2 moles of [tex]\( HCl \)[/tex].
2. Determine Moles of [tex]\( HCl \)[/tex] Used:
You have 35.9 mL of 0.026 M [tex]\( HCl \)[/tex]. First, convert the volume from mL to L by dividing by 1000:
[tex]\[ 35.9 \, \text{mL} = 0.0359 \, \text{L} \][/tex]
Calculate the moles of [tex]\( HCl \)[/tex] using the formula:
[tex]\[ \text{moles of } HCl = \text{Molarity} \times \text{Volume (L)} \][/tex]
[tex]\[ \text{moles of } HCl = 0.026 \, \text{M} \times 0.0359 \, \text{L} = 0.0009334 \, \text{moles} \][/tex]
3. Relate Moles of [tex]\( HCl \)[/tex] to Moles of [tex]\( Ca(OH)_2 \)[/tex]:
According to the balanced equation, 2 moles of [tex]\( HCl \)[/tex] react with 1 mole of [tex]\( Ca(OH)_2 \)[/tex]. Therefore, divide the moles of [tex]\( HCl \)[/tex] by 2 to find moles of [tex]\( Ca(OH)_2 \)[/tex]:
[tex]\[ \text{moles of } Ca(OH)_2 = \frac{0.0009334}{2} = 0.0004667 \, \text{moles} \][/tex]
4. Calculate Concentration of [tex]\( Ca(OH)_2 \)[/tex]:
The volume of the [tex]\( Ca(OH)_2 \)[/tex] solution is 25.0 mL. Convert this to liters:
[tex]\[ 25.0 \, \text{mL} = 0.0250 \, \text{L} \][/tex]
Find the concentration using the formula:
[tex]\[ \text{Concentration (M)} = \frac{\text{moles}}{\text{Volume (L)}} \][/tex]
[tex]\[ \text{Concentration of } Ca(OH)_2 = \frac{0.0004667}{0.0250} = 0.018668 \, \text{M} \][/tex]
So, the concentration of the saturated [tex]\( Ca(OH)_2 \)[/tex] solution is approximately 0.01867 M.
