Consider 1.00 L of the buffer system that contains 0.200 M hydrocyanic acid(HCN) and 0.150 M sodium cyanide (NaCN). The pKa of hydrocyanic acid is 9.31.
What is the [CN-] after 0.020 mol of HCl is added?
I work these problems with millimoles.
mmols HCN = mL x M = 1000 mL x 0.200 M = 200
mmols NaCN = 1000 mL x 0.150 = 150
.....................CN^- + H^+ ==> HCN
Initial.............150.....................200
add............................20.......................
change..........-20......-20............+20
equilibrium...130.........0..............220
(CN^-) = M = millimoles/mL = 130/1000 = ? assuming the HCl is added as a gas. If added as an aqueous solution, then total mL will be 1000 + ? mL added solution.
Post your work if you get stuck.
To find the [CN-] after adding HCl, we need to consider the reaction that takes place between hydrocyanic acid (HCN) and hydrochloric acid (HCl). HCN reacts with HCl to form H3O+ (hydronium ion) and CN- (cyanide ion). The reaction can be represented as follows:
HCN + HCl → H3O+ + CN-
To solve this problem, we can use the Henderson-Hasselbalch equation. The Henderson-Hasselbalch equation relates the pH of a solution to the pKa of the acid and the ratio of the concentration of the acid and its conjugate base.
pH = pKa + log([A-]/[HA])
In this case, HCN is the acid (HA) and CN- is its conjugate base (A-). We are given the pKa of HCN as 9.31. We can calculate the initial concentrations of HCN and CN- using the initial volumes and concentrations given.
Initial concentration of HCN = 0.200 M
Initial concentration of CN- = 0.150 M
To calculate the concentrations of HCN and CN- after the addition of HCl, we need to consider the stoichiometry of the reaction.
Given that 0.020 mol of HCl is added, and the balanced equation tells us that HCN and HCl react in a 1:1 ratio, we know that 0.020 mol of HCN will react, and an equal amount (0.020 mol) of CN- will be produced.
Now, we can determine the final concentrations of HCN and CN-. The final concentration of HCN can be calculated by subtracting the amount reacted (0.020 mol) from the initial concentration of HCN, and the final concentration of CN- can be calculated by adding the amount produced (0.020 mol) to the initial concentration of CN-.
Final concentration of HCN = Initial concentration of HCN - amount reacted
Final concentration of CN- = Initial concentration of CN- + amount produced
Final concentration of HCN = 0.200 M - 0.020 mol/L
Final concentration of CN- = 0.150 M + 0.020 mol/L
Now, we can substitute these values into the Henderson-Hasselbalch equation to find the pH of the buffer solution after the addition of HCl.
pH = 9.31 + log([CN-]/[HCN])
Substituting the values for [CN-] and [HCN], we can solve for the pH.