If 0.10 M potassium chromate is slowly added to a solution containing 0.50 M AgNO3 and 0.50 M Ba(NO3)2. What is the Ag+ concentration when BaCrO4 just starts to precipitate? The Ksp for Ag2CrO4 and BaCrO4 are 1.1 x 10-12 and respectively.
To find the Ag+ concentration when BaCrO4 just starts to precipitate, we need to calculate the concentration of Ag+ ions in the solution.
First, let's write down the balanced chemical equation for the precipitation reaction:
AgNO3 + BaCrO4 → Ag2CrO4 + Ba(NO3)2
We know the initial concentration of AgNO3 is 0.50 M, and we want to find the Ag+ concentration when BaCrO4 just starts to precipitate. This means all the Ba2+ ions would react with the CrO4-2 ions to form BaCrO4.
Therefore, the concentration of CrO4-2 ions can be determined using the stoichiometry of the reaction.
The stoichiometry of the reaction tells us that 1 mole of BaCrO4 is formed for every 1 mole of Ba2+ ion reacts. Since the initial concentration of Ba(NO3)2 is 0.50 M, the concentration of Ba2+ ions is also 0.50 M.
Now, let's calculate the concentration of CrO4-2 ions using the initial concentration of K2CrO4, which is 0.10 M.
Since potassium chromate (K2CrO4) dissociates into 2 K+ ions and 1 CrO4-2 ion, the concentration of CrO4-2 ions in the solution is given by:
0.10 M × (1 mol CrO4-2 / 1 mol K2CrO4) = 0.10 M
Since Ag2CrO4 has a Ksp value of 1.1 × 10^-12, we can set up an equilibrium expression:
Ksp = [Ag+]^2 [CrO4-2]
Since the concentration of Ag+ ions is initially zero, the equilibrium concentration can be represented as:
Ksp = (x)^2 (0.10 M)
Substituting the Ksp for Ag2CrO4:
(1.1 × 10^-12) = (x)^2 (0.10 M)
Solving for x, the concentration of Ag+ ions:
x = sqrt((1.1 × 10^-12) / (0.10 M))
x = 1.05 × 10^-6 M
Therefore, the Ag+ concentration when BaCrO4 just starts to precipitate is approximately 1.05 × 10^-6 M.
To find the Ag⁺ concentration when BaCrO₄ just starts to precipitate, we need to determine the point at which the concentrations of Ag⁺ and CrO₄²⁻ ions reach the solubility product constant (Ksp) for BaCrO₄.
Here's how we can approach this problem step by step:
Step 1: Write the balanced chemical equation for the reaction that occurs when potassium chromate (K₂CrO₄) is added to the solution containing AgNO₃ and Ba(NO₃)₂:
2 AgNO₃ + K₂CrO₄ → Ag₂CrO₄ + 2 KNO₃
This equation shows that two moles of AgNO₃ react with one mole of K₂CrO₄ to form one mole of Ag₂CrO₄.
Step 2: Calculate the initial concentration of Ag⁺ ions before any reaction occurs:
The solution initially contains 0.50 M AgNO₃, so the concentration of Ag⁺ ions is also 0.50 M.
Step 3: Determine the concentration of CrO₄²⁻ ions required for precipitation of BaCrO₄:
The solubility product constant (Ksp) for BaCrO₄ is not given in the question. Please provide the value of Ksp for BaCrO₄.
Once you have the value of Ksp for BaCrO₄, we can proceed to determine the concentration of CrO₄²⁻ ions needed for precipitation.
Step 4: Use the balanced chemical equation and stoichiometry to relate the concentrations of Ag⁺ and CrO₄²⁻ ions:
According to the balanced equation, 2 moles of Ag⁺ ions are required for the formation of 1 mole of Ag₂CrO₄. This means that the concentration of Ag⁺ ions and CrO₄²⁻ ions will change in a 1:2 ratio.
Step 5: Calculate the concentration of CrO₄²⁻ ions required for AgCrO₄ to reach its solubility product constant:
Using the 1:2 stoichiometric ratio, we multiply the initial concentration of Ag⁺ ions by 2 to find the concentration of CrO₄²⁻ ions needed for precipitation.
Step 6: Compare the calculated concentration of CrO₄²⁻ ions with the solubility product constant (Ksp) for BaCrO₄:
If the concentration of CrO₄²⁻ ions calculated in the previous step is greater than the solubility product constant (Ksp) for BaCrO₄, then precipitation of BaCrO₄ occurs and Ag⁺ ions will start to react to form Ag₂CrO₄.
Step 7: Calculate the concentration of Ag⁺ ions remaining after the reaction:
Subtract the concentration of Ag⁺ ions consumed in the reaction (twice the concentration of CrO₄²⁻ ions) from the initial concentration of Ag⁺ ions to find the remaining concentration of Ag⁺ ions.
Following these steps, you should be able to determine the Ag⁺ concentration when BaCrO₄ just starts to precipitate once the Ksp value for BaCrO₄ is provided.