Calculate the pH of a 0.18 M solution of cyanide ion, CN- given the
Ka (HCN) = 6.2 x 10^-10.
I know how to calculate Ka and Kb values no problem, but I don't know which value to use in my calculations. Is it based on the conjugate base/acid formed or hydronium or hydroxide ions formed?
I'm wondering, if Hydronium ions are formed , do we use Ka? And vice versa (OH- we use Kb?
When calculating the pH of a solution, you need to consider the concentration of the relevant ions. In this case, we are dealing with the cyanide ion, CN-.
The CN- ion is the conjugate base of the weak acid, HCN. Given the Ka value for HCN (6.2 x 10^-10), we can assume that the dissociation of HCN is very limited.
To find the pH of a solution of CN-, we need to consider the reaction between CN- and water. This results in the formation of OH- ions.
The reaction can be written as:
CN- + H2O ⇌ HCN + OH-
Since the concentration of OH- ions is dependent on the concentration of CN- ions, we can use the pOH equation to find their concentration:
pOH = -log[CN-]
Since the solution is neutral, the concentration of OH- ions will be equal to the concentration of H+ ions. Thus, the pH can be calculated as:
pH = 14 - pOH = 14 - (-log[CN-]) = 14 + log[CN-]
Therefore, to calculate the pH of the 0.18 M solution of CN-, plug the concentration into the equation:
pH = 14 + log[0.18]
Using a calculator, we find:
pH ≈ 13.75
To calculate the pH of a solution, you need to consider the concentration of the hydronium ions (H3O+) present in the solution. In this case, we are given the concentration of the cyanide ion (CN-), which is the conjugate base of hydrocyanic acid (HCN).
To find the concentration of H3O+ ions, we need to consider the reaction between HCN and water:
HCN + H2O <=> H3O+ + CN-
Since cyanide ion (CN-) is the conjugate base of HCN, it is a weak base. Therefore, we need to consider Kb (base dissociation constant) instead of Ka (acid dissociation constant) for this reaction. Kb represents the equilibrium constant for the reaction of the base with water.
The relationship between Ka and Kb is given by the equation:
Ka x Kb = Kw
where Kw is the ion product of water (1.0 x 10^-14 at 25°C).
Since we are not provided with the Kb value directly, we can use this relationship to determine it. Rearranging the equation, we have:
Kb = Kw / Ka
Kw is a constant value, and Ka (given as 6.2 x 10^-10) can be plugged into the equation to obtain Kb.
Once you have the Kb value, you can then proceed to calculate the concentration of the hydroxide ions (OH-) formed. Since pOH = -log [OH-], you can find the pOH and then convert it to pH using the equation:
pH + pOH = 14
where 14 is the pH scale constant.
So, to summarize the steps:
1. Calculate Kb using the equation: Kb = Kw / Ka
2. Use Kb to find the concentration of OH- ions formed.
3. Find the pOH using pOH = -log [OH-].
4. Calculate the pH using pH + pOH = 14.
Remember to pay attention to units and conversions throughout the calculations.