f 27.0 mL of Ca(OH)2 with an unknown concentration is neutralized by 32.40 mL of 0.185 M HCl, what is the concentration of the Ca(OH)2 solution? Show all of the work needed to solve this problem.
Ca(OH)2 + 2 HCl 2 H2 O + CaCl2.
Ca(OH)2 + 2HCl ==> 2H2O + CaCl2.
1. moles HCl = M x L = ??
2. Using the coefficients in the balanced equation, convert moles HCl to moles Ca(OH)2.
3. Then M Ca(OH)2 = moles Ca(OH)2/L Ca(OH)2
To find the concentration of the Ca(OH)2 solution, we can use the concept of stoichiometry and the equation given: Ca(OH)2 + 2 HCl → 2 H2O + CaCl2.
Step 1: Calculate the number of moles of HCl used.
Given that the volume of HCl used is 32.40 mL (or 0.03240 L), and the molarity of HCl is 0.185 M, we can use the formula:
moles of HCl = Volume (L) × Concentration (M)
moles of HCl = 0.03240 L × 0.185 M
Step 2: Determine the moles of Ca(OH)2 that react with the moles of HCl.
From the balanced equation, we can see that 1 mol of Ca(OH)2 reacts with 2 moles of HCl. Therefore, the moles of Ca(OH)2 can be calculated as follows:
moles of Ca(OH)2 = (moles of HCl) / (2 moles of HCl per 1 mol of Ca(OH)2)
Step 3: Calculate the concentration of Ca(OH)2 solution.
The concentration of Ca(OH)2 solution can be calculated using the formula:
concentration (M) = moles / volume (L)
In this case, the volume of Ca(OH)2 solution is given as 27.0 mL (or 0.0270 L). Using the moles of Ca(OH)2 calculated in the previous step, we can find the concentration of the Ca(OH)2 solution.
concentration (Ca(OH)2) = (moles of Ca(OH)2) / (volume of Ca(OH)2 solution)
Now let's perform the calculations step by step:
Step 1:
moles of HCl = 0.03240 L × 0.185 M
moles of HCl = 0.005994 mol
Step 2:
moles of Ca(OH)2 = (moles of HCl) / (2 moles of HCl per 1 mol of Ca(OH)2)
moles of Ca(OH)2 = 0.005994 mol / 2
moles of Ca(OH)2 = 0.002997 mol
Step 3:
concentration (Ca(OH)2) = (moles of Ca(OH)2) / (volume of Ca(OH)2 solution)
concentration (Ca(OH)2) = 0.002997 mol / 0.0270 L
Finally, let's divide the moles by the volume to get the concentration:
concentration (Ca(OH)2) = 0.111 M
Therefore, the concentration of the Ca(OH)2 solution is 0.111 M.