Calculate the mass (in mg) of KCN needed to make 500. mL of aqueous KCN solution with a pH of 10.00. The Ka of HCN = 5.0 x 10-10. I got the answer 7.8 mg but it's wrong. Can someone please explain how to do it?

pH = 10; pOH = 4

.......CN^- + HOH ==> HCN + OH^-
E......x.............1E-4...1E-4
Kb for KCN = (Kw/Ka for HCN) = (1E-4)(1E-4)/x
Solve for x = KCN in mols/L.
To make 500 mL is 1/2 that. Then
mols = g/molar mass. You know mols and molar mass, solve for g and convert to mg.

Nevermind! I realized I was multiplying by the CN- molar mass instead of KCN.

i'm so sad

To calculate the mass of KCN needed to make a given volume of solution with a specific pH, we need to first understand the relationship between pH, pKa, and the concentration of the acid and its conjugate base.

In this case, we are dealing with the weak acid HCN and its conjugate base KCN. The equilibrium reaction for HCN is as follows:

HCN + H2O ⇌ CN- + H3O+

The expression for the acid dissociation constant (Ka) is given by:

Ka = [CN-][H3O+]/[HCN]

Since we are given the value of Ka (5.0 x 10-10), we can assume that the concentration of HCN and CN- will be equal (as KCN will fully dissociate in water). Hence:

[CN-] = [HCN]

Now, we need to find the concentration of CN- ions required to achieve a pH of 10.00. pH is defined as the negative logarithm of the concentration of H3O+ (or [H+]) ions:

pH = -log[H3O+]

Since we are given a pH of 10.00, we can calculate the concentration of H3O+ ions using the reverse of the pH formula:

[H3O+] = 10^(-pH)

[H3O+] = 10^(-10.00)

[H3O+] = 1.0 x 10^(-10)

Since [H3O+] is equal to [HCN] (because of the stoichiometry), we find that [HCN] = 1.0 x 10^(-10) mol/L.

Now, we proceed to calculate the mass of KCN required to make 500 mL of aqueous KCN solution. To do this, we need to convert the concentration to milligrams:

Concentration (in mg/mL) = Concentration (in mol/L) × Molar mass (in mg/mol)

Molar mass of KCN = The sum of the atomic masses of K (39.10 g/mol) + C (12.01 g/mol) + N (14.01 g/mol)

Molar mass of KCN = 39.10 + 12.01 + 14.01 = 65.12 g/mol

Now we can calculate the mass:

Mass of KCN (in mg) = Concentration (in mg/mL) × Volume (in mL)

Mass of KCN (in mg) = Concentration (in mg/mL) × 500 mL

Substituting the values, we have:

Mass of KCN (in mg) = (1.0 x 10^(-10) mg/mL) × 500 mL

Mass of KCN (in mg) = 5.0 x 10^(-8) mg

Therefore, the correct mass of KCN needed to make a 500 mL aqueous KCN solution with pH 10.00 is 5.0 x 10^(-8) mg.