[Borek]

1.000 g of potassium ferrocyanide was gently fused with the excess potassium carbonate in the inert atmosphere. Solid after fusion was dissolved in a concentrated sulfuric acid and evolving gases were absorbed in the solution of barium hydroxide. After filtration pH of the solution was brought to 11.5 with a nitric acid, mixed with a solution containing exactly 2.000 g of silver nitrate and diluted to 250 mL. Assuming all reactions were stoichiometric, was the final solution clear, or did it contain a precipitate?

Note: assuming you understand the chemistry behind the question, you don't need values of any equilibrium constants to find the answer.

[XGen]

Allow me to clarify if I am understanding the question correctly.

In the beginning, potassium ferrocynanide is fused with potassium carbonate. This fused solid is then dissolved in a concentrated sulfuric acid, and the gases evolved are absorbed in a solution of barium hydroxide. This solution that contained (before) the barium hydroxide is then filtered, and had its pH lowered with nitric acid. The new solution is then mixed with a solution containing 2.000g of silver nitrate, and then this solution is diluted to 250 mL.

[Borek]

Yes.

[UG]

Let's see if I got these reactions correct. So I had a look around and it appears potassium ferrocyanide and potassium carbonate produces potassium cyanide. I assume the reaction is:
K₄Fe(CN)₆ + K₂CO₃  6KCN + FeO + CO₂
Then I thought dissolving the solid KCN in concentrated sulfuric acid would give hydrogen cyanide gas in a 1:1 ratio. The hydrogen cyanide then reacts with barium hydroxide to give barium cyanide? The pH of the barium cyanide is then lowered with nitric acid, giving HCN again? This was then reacted with silver nitrate and depending on whether HCN is excess or not, a soluble complex may form?

[Borek]

You are mostly right, but you missed two precipitates - one is sure and was filtered out, the other is what the question is about.

The pH of the barium cyanide is then lowered with nitric acid, giving HCN again?

At pH 11.5 most of the cyanides is in the form of CN^- (compare this post, pKa for HCN is 9.3). pH is lowered to make sure OH^- will not interfere reacting with ailver.

[UG]

Are they BaSO₄ and AgCN?
I calculated number of moles of CN^- as 0.016289 mol and the number of moles of Ag⁺ as 0.011774 mol. So there isn't enough CN^- to form [Ag(CN)₂]^- therefore there will be a precipitate?

[Borek]

Are they BaSO₄

There was no sulfur in the original mixture.

AgCN?

Right.

I calculated number of moles of CN^- as 0.016289 mol and the number of moles of Ag⁺ as 0.011774 mol. So there isn't enough CN^- to form [Ag(CN)₂]^- therefore there will be a precipitate?

Yes.

This system (Ag⁺/Ag(CN)₂^-/AgCN) is used to determine cyanides by a titration with the silver nitrate. As long as there is enough cyanides in the solution addition of Ag⁺ produces soluble Ag(CN)₂^-. When you add an excess of Ag⁺ precipitate forms immediately, and solution becomes cloudy - that's the end point.