What is the pH of a solution prepared by mixing 50.0 mL of 0.010 mol/L HCl(aq) and 50.0 mL of 0.010 Ca(OH)2(aq)?
Assume the temperature is 25 degrees celsius, where Kw = 1.0 x 10^-14 at 25 degrees celsius.
To find the pH of the solution, we need to calculate the concentration of the resulting H+ ions after mixing the two solutions.
Step 1: Calculate the moles of HCl:
Using the formula:
moles = concentration (mol/L) × volume (L)
moles of HCl = 0.010 mol/L × 0.050 L
moles of HCl = 0.0005 mol
Step 2: Calculate the moles of Ca(OH)2:
Since Ca(OH)2 dissociates into 2 moles of OH- ions, we need to calculate the moles of OH-.
moles of OH- = 2 × 0.010 mol/L × 0.050 L
moles of OH- = 0.001 mol
Step 3: Determine the limiting reactant:
The limiting reactant is the one that is completely consumed in the reaction, limiting the formation of product. In this case, the OH- ions from Ca(OH)2 will react with the H+ ions from HCl to form water.
Since we have an equal number of moles of H+ and OH- ions, neither reactant is in excess. So, the limiting reactant is either H+ or OH-, and both will react completely.
Step 4: Determine the moles of H+ ions left after the reaction:
Since H+ and OH- ions react in a 1:1 ratio, the moles of H+ ions left after the reaction is:
moles of H+ ions = initial moles of H+ ions - moles of OH- ions
moles of H+ ions = 0.0005 mol - 0.001 mol
moles of H+ ions = -0.0005 mol
Note: A negative value indicates that all H+ ions reacted with OH- ions to form water. The solution is basic.
Step 5: Calculate the concentration of H+ ions:
To find the concentration of H+ ions, divide the moles of H+ ions by the total volume of the solution:
concentration of H+ ions = moles of H+ ions / total volume (L)
total volume = 0.050 L (HCl) + 0.050 L (Ca(OH)2)
total volume = 0.100 L
concentration of H+ ions = (-0.0005 mol) / 0.100 L
concentration of H+ ions = -0.005 mol/L
Note: A negative concentration indicates a basic solution.
Step 6: Calculate the pOH:
To find the pOH of the solution, use the formula:
pOH = -log10 (concentration of OH- ions)
Since the concentration of OH- ions is 0.010 mol/L (from Ca(OH)2), we have:
pOH = -log10 (0.010) = 2
Step 7: Calculate the pH:
Since pH + pOH = 14 (at 25 degrees Celsius), we can calculate the pH:
pH = 14 - pOH
pH = 14 - 2
pH = 12
The pH of the solution prepared by mixing 50.0 mL of 0.010 mol/L HCl(aq) and 50.0 mL of 0.010 Ca(OH)2(aq) is 12.