What is the pH of a solution prepared by mixing 500mL of 2.0M HCN (Ka= 4.9x10^-10) with 500mL of 1.0 M KOH?
HCN + KOH ==> KCN + H2O
mols HCN = ?
mols KOH = ?
How much HCN formed?
How much HCN left over.
Use the Henderson-Hasselbalch equation to solve for pH.
Post your work if you get stuck.
To find the pH of the solution prepared by mixing HCN and KOH, we need to determine the concentration of the resulting solution and then calculate its pH using the appropriate formula.
Step 1: Calculate the moles of HCN and KOH.
First, we calculate the moles of HCN by using the formula:
moles = concentration (M) x volume (L)
moles of HCN = 2.0 M x 0.5 L (500 mL converted to 0.5 L)
moles of HCN = 1.0 mole
Similarly, we calculate the moles of KOH:
moles of KOH = 1.0 M x 0.5 L
moles of KOH = 0.5 mole
Step 2: Determine the limiting reagent.
To determine the limiting reagent, we compare the mole ratios of HCN to KOH. In this case, the ratio is 1:1. Since both HCN and KOH are present in stoichiometric amounts, neither is in excess or limiting. Thus, we do not need to perform any further calculations to determine the limiting reagent.
Step 3: Determine the moles of H2O produced.
Since the reaction between HCN and KOH results in the formation of water (H2O), we can assume that the volume of water formed is the sum of the volumes of the two solutions mixed together:
Volume of water = volume of HCN + volume of KOH
Volume of water = 500 mL + 500 mL
Volume of water = 1000 mL (or 1 L)
Step 4: Calculate the concentration of the resulting solution.
To calculate the concentration of the resulting solution (HCN + KOH), we need to consider the final volume after mixing, which is 1 L (since 500 mL + 500 mL = 1000 mL = 1 L). Since we know the moles of each component (HCN and KOH), we can calculate their total moles:
total moles = moles of HCN + moles of KOH
total moles = 1.0 mole + 0.5 mole
total moles = 1.5 moles
Now, we can calculate the resulting concentration:
final concentration (M) = total moles / final volume (L)
final concentration = 1.5 moles / 1 L
final concentration = 1.5 M
Step 5: Calculate the pOH.
To find the pOH, we need to use the concentration of hydroxide ions (OH-) in the solution, which is given by the concentration of KOH. Since the concentration of KOH is 1.0 M, the concentration of OH- is also 1.0 M. The pOH can be calculated using the formula:
pOH = -log[OH-]
pOH = -log(1.0)
pOH = 0
Step 6: Calculate the pH.
To calculate the pH, we use the relationship:
pH + pOH = 14
pH = 14 - pOH
pH = 14 - 0
pH = 14
Therefore, the pH of the solution prepared by mixing 500 mL of 2.0 M HCN with 500 mL of 1.0 M KOH is 14.