What is the pH of a 2.62 x 10^-1 HCN solution? The pKa for HCN = 9.212
I don't know whether to use the Henderson Hasselbalch Equation or just convert pKa to Ka and work it out that way.
To determine the pH of a solution of HCN (hydrogen cyanide), you can use the Henderson-Hasselbalch equation or convert pKa to Ka and work it out that way. Here's a step-by-step process for both methods:
Method 1: Using the Henderson-Hasselbalch equation
Step 1: Write down the Henderson-Hasselbalch equation:
pH = pKa + log([A-]/[HA])
Step 2: Identify the relevant values:
pKa = 9.212 (given)
[HA] = concentration of the acidic form (HCN) = 2.62 x 10^-1
Step 3: Calculate the concentration of the conjugate base ([A-]):
[A-] = 10^(-pKa) x [HA]
[A-] = 10^(-9.212) x (2.62 x 10^-1)
[A-] = 1.55 x 10^-10
Step 4: Substitute the values into the Henderson-Hasselbalch equation and solve for pH:
pH = 9.212 + log((1.55 x 10^-10) / (2.62 x 10^-1))
pH ≈ 9.212 - 9.61
pH ≈ -0.398
Therefore, the pH of the 2.62 x 10^-1 HCN solution is approximately -0.398.
Method 2: Converting pKa to Ka
Step 1: Convert pKa to Ka:
Ka = 10^(-pKa)
Ka = 10^(-9.212)
Step 2: Calculate [H+] concentration using the dissociation of HCN:
Ka = [H+][A-] / [HA]
[H+] = Ka x [HA] / [A-]
[H+] = 10^(-9.212) x (2.62 x 10^-1) / (1.55 x 10^-10)
[H+] ≈ 4.43 x 10^-8
Step 3: Calculate pH using the definition of pH:
pH = -log[H+]
pH ≈ -log(4.43 x 10^-8)
pH ≈ 7.354
Therefore, the pH of the 2.62 x 10^-1 HCN solution is approximately 7.354.
Both methods should give you similar results, but it's always good to double-check using different approaches.
To determine the pH of a solution, you can use either the Henderson-Hasselbalch equation or convert the pKa value to Ka and solve for the hydronium ion concentration (H3O+). Let me explain both methods to you, and you can choose which one you would like to use.
Method 1: Using 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 (HCN) to its conjugate base (CN-). The equation is as follows:
pH = pKa + log10 ([A-]/[HA])
In this case, the acid is HCN and its dissociation can be represented as follows:
HCN ⇌ H+ + CN-
Since the solution contains only HCN and no CN-, we can assume that the concentration of CN- is negligible compared to HCN. Therefore, the equation simplifies to:
pH = pKa + log10 ([HCN]/[CN-])
To solve this equation, you need to know the values of pKa and [HCN]. Given that pKa = 9.212 and [HCN] = 2.62 x 10^-1, you can substitute these values into the equation to calculate the pH.
Method 2: Converting pKa to Ka
If you prefer to convert the pKa value to Ka and solve for the hydronium ion concentration (H3O+), you can follow these steps:
Step 1: Calculate Ka (acid dissociation constant) from pKa using the following equation:
Ka = 10^(-pKa)
Step 2: Set up an equation for the dissociation of HCN:
HCN ⇌ H+ + CN-
Let's assume the initial concentration of HCN is [HCN], and at equilibrium, the concentration of H+ is [H+].
The equilibrium expression for Ka is given by:
Ka = [H+][CN-] / [HCN]
Since [CN-] is negligible compared to [HCN], we can assume that [H+] = [HCN]. Therefore, we can simplify the equation to:
Ka = [H+]^2 / [HCN]
Step 3: Rearrange the equation to solve for [H+]:
[H+] = sqrt(Ka * [HCN])
Finally, you can substitute the values of Ka and [HCN] into the equation to calculate [H+], and then convert it to pH using the equation pH = -log[H+].
Both methods will yield the same pH value for the given HCN solution. Choose the method you feel most comfortable with or simulate both methods for practice.