A 29.8 mL sample of a 0.476 M aqueous hydrocyanic acid solution is titrated with a 0.487 M aqueous barium hydroxide solution. What is the pH at the start of the titration, before any barium hydroxide has been added

The pH is 4.76

Explanation:

Step 1: Data given

Volume of a 0.476 M hydrocyanic acid solution = 29.8 mL = 0.0298 L

Volume of 0.487 M barium hydroxide solution = ?

Ka HCN = 6.2 * 10^-10

Step 2: Calculate pH

Hydrocyanic acid is a weak acid.

Barium hydroxide is a strong base.

The question asked = the pH BEFORE any base has been added, so we can ignore the base.  

To calculate the pH of aweak acid, we need the pKa

HCN ⇔ H+ + CN-

Ka =  [H+][CN-]/[HCN]

⇒ for weak acid: [H+]=[CN-]

Ka = [H+]²/[HCN]

[H+]² = [HCN]*Ka

[H+] = √([HCN]*Ka)

pH = -log(√([HCN]*Ka))

pH = -log(√(0.476 * 6.2*10^-10))

pH = 4.76

The pH is 4.76