a sample of 20.0 mL of 0.100 M HCN (Ka=6.2*10^-10) is titrated with 0.150 M NaOH.
a) what volume of NaOH is used in this titration to reach the equivalence point?
b) What is the molar concentration of CN- at the equivalence point?
c) What is the pH of the solution at the equivalence point?
d) What is the pH of this solution when only 6.667 mL of the 0.150 M NaOH is added to 20.0 mL of the 0.100 M HCN?
To answer these questions, we need to follow the steps of a titration calculation:
Step 1: Write the balanced chemical equation for the reaction between HCN and NaOH.
Step 2: Calculate the number of moles of HCN initially in the 20.0 mL solution.
Step 3: Use the stoichiometry from the balanced equation to determine the number of moles of NaOH required to reach the equivalence point.
Step 4: Convert the moles of NaOH to the volume using the concentration of NaOH.
Step 5: Calculate the concentration of CN- at the equivalence point using the stoichiometry of the balanced equation.
Step 6: Calculate the pH at the equivalence point using the dissociation constant (Ka) of HCN.
Step 7: Calculate the pH of the solution after adding 6.667 mL of the 0.150 M NaOH to the 20.0 mL of 0.100 M HCN.
Now let's go through each question step by step:
a) What volume of NaOH is used in this titration to reach the equivalence point?
Step 1: The balanced chemical equation for the reaction between HCN and NaOH is:
HCN + NaOH → NaCN + H2O
Step 2: Calculate the number of moles of HCN initially in the 20.0 mL solution.
moles of HCN = volume (in L) × concentration (in M)
moles of HCN = 20.0 mL × (1 L/1000 mL) × 0.100 M
Step 3: Use the stoichiometry from the balanced equation to determine the number of moles of NaOH required to reach the equivalence point.
From the balanced equation, 1 mole of HCN reacts with 1 mole of NaOH.
So, the number of moles of NaOH required is equal to the moles of HCN.
Step 4: Convert the moles of NaOH to the volume using the concentration of NaOH.
volume of NaOH = moles of NaOH / concentration of NaOH
b) What is the molar concentration of CN- at the equivalence point?
Step 5: Calculate the concentration of CN- at the equivalence point using the stoichiometry of the balanced equation.
Since the reaction between HCN and NaOH has a 1:1 stoichiometry, the concentration of CN- at the equivalence point is equal to the concentration of NaOH.
c) What is the pH of the solution at the equivalence point?
Step 6: Calculate the pH at the equivalence point using the dissociation constant (Ka) of HCN.
The equilibrium expression for the dissociation of HCN is:
Ka = [H+][CN-] / [HCN]
At the equivalence point, all the HCN has reacted with NaOH, and only NaCN is left.
So, the concentration of CN- is the same as the initial concentration of NaOH.
Use the equation above to find the concentration of H+ (which is equal to [H+]) and then calculate the pH using the equation pH = -log[H+].
d) What is the pH of this solution when only 6.667 mL of the 0.150 M NaOH is added to 20.0 mL of the 0.100 M HCN?
Step 7: Calculate the pH of the solution after adding 6.667 mL of the 0.150 M NaOH to the 20.0 mL of 0.100 M HCN.
This is a stoichiometric calculation, assuming that all the HCN reacts with NaOH. Subtract the moles of HCN that reacted from the initial moles of HCN and NaOH, then calculate the new concentration of HCN. Use the same steps mentioned in question c) to find the pH of the solution at this point.
By following these steps, you should be able to calculate the answers to all four questions.