Show, with equations, why the solution from which BaSO4 is precipitated cannot be allowed to be more than 0.01-0.05M in HCl.
Because both hydogens in H2SO4 are not strong acids. The first H ionizes completely (100%) so that 0.1M H2SO4 gives 0.1M H^+ and 0.1M HSO4^-. BUT the second H ion is not a strong acid (although it is relatively strong as weak acids go) and
HSO4^- ==> H^+ + SO4^2- with k2 = about 0.012.
So what happens is this.
BaSO4(s) ==> Ba^2+ + SO4^2-
If HCl is present, the H^+ from the strong (100% ionized) HCl, combines with the very small amount of SO4^2- to form the HSO4^- with the resulting k2. Now what happens with Le Chatelier's Principle? If H^+ is increased, HSO4^- forms, and the first reaction I showed moves to the right which increases the solubility of BaSO4. So if H^+ is too high, the solubility of BaSO4 is increased to the point that too much is lost due to solubility and the results for Ba^2+ or SO4^2- (depending upon which is being determined) will be too low. I have seen some calculations (and done some myself) and it is easy to lose as much as 1 mg BaSO4 and in many cases that is too much.
I would love to see the equation of BaSO4 loss due to the increased HCl! 😁
To understand why the solution from which BaSO4 is precipitated cannot be allowed to be more than 0.01-0.05M in HCl, we need to consider the solubility equilibrium of barium sulfate in the presence of HCl.
The solubility equilibrium of barium sulfate (BaSO4) can be represented by the following equation:
BaSO4(s) ⇌ Ba2+(aq) + SO42-(aq)
According to the solubility product constant (Ksp) expression for barium sulfate, the equilibrium expression is:
Ksp = [Ba2+][SO42-]
Now, when hydrochloric acid (HCl) is added to the solution, it dissociates into hydrogen ions (H+) and chloride ions (Cl-):
HCl(aq) ⇌ H+(aq) + Cl-(aq)
The hydrogen ions (H+) can react with the sulfate ions (SO42-) from the barium sulfate, resulting in the formation of sulfuric acid (H2SO4) according to the following reaction:
H+(aq) + SO42-(aq) ⇌ H2SO4(aq)
The presence of excess HCl can shift the equilibrium towards the production of H2SO4, which can then protonate the barium ions (Ba2+), resulting in the dissolution of barium sulfate.
However, the solubility product constant (Ksp) of barium sulfate is very small (around 1.1 x 10^-10), meaning it has a very low solubility. To ensure the precipitation of barium sulfate, the concentration of barium ions (Ba2+) and sulfate ions (SO42-) in the solution should be kept below a certain threshold.
If the concentration of HCl is too high (above 0.01-0.05M), it can significantly increase the concentration of hydrogen ions (H+) in the solution, which can then react with sulfate ions (SO42-) from BaSO4, leading to the dissolution of the precipitate.
Therefore, to maintain the precipitation of barium sulfate and prevent its dissolution, it is essential to keep the concentration of HCl in the solution below the specified range (0.01-0.05M).
To understand why the solution from which BaSO4 is precipitated should not exceed 0.01-0.05M in HCl, let's analyze the relevant chemical reactions involved.
When barium chloride (BaCl2) reacts with sulfuric acid (H2SO4), it forms barium sulfate (BaSO4) and hydrochloric acid (HCl):
BaCl2 + H2SO4 → BaSO4 + 2HCl
The formation of BaSO4 is the precipitation reaction of interest in this case. The solubility product constant, Ksp, is a measure of the equilibrium solubility of a compound. For BaSO4, its solubility product is given by:
Ksp = [Ba2+][SO4^2-]
Generally, when a precipitate is forming, the concentration of the ions involved should exceed the Ksp value to drive the reaction toward product formation. However, precipitation reactions are often limited by additional factors such as the common ion effect.
In this case, the excess HCl present affects the equilibrium by introducing a high concentration of chloride ions (Cl-) into the solution. These chloride ions can react with the barium ions (Ba2+) to form less soluble barium chloride (BaCl2):
Ba2+ + 2Cl- → BaCl2
Since barium chloride is more soluble than barium sulfate, this reaction depletes the amount of barium ions available to react with sulfate ions, consequently reducing the formation of BaSO4.
To determine the acceptable concentration range of HCl, we need to consider the reaction that consumes the barium ions most efficiently, which is the reaction between barium ions and chloride ions. The equilibrium constant for this reaction can be represented as:
K = [BaCl2]/[Ba2+][Cl-]²
From this, it follows that [Ba2+] = [Cl-]²/K
Since we want to keep the precipitation of BaSO4 significant, the concentration of barium ions should not be too small, i.e., [Ba2+] > Ksp. Substituting the expression for [Ba2+] from the equation above:
Ksp < [Cl-]²/K
Simplifying, we obtain:
[Cl-]² > Ksp * K
Since [Cl-] is essentially equal to the initial HCl concentration, we have:
[HCl] > √(Ksp * K)
The value of Ksp for BaSO4 is approximately 1.1 x 10^(-10) at 25°C. The value of K for barium ions and chloride ions can be determined experimentally but is typically around 1 x 10^3.
Substituting these values, we find:
[HCl] > √(1.1 x 10^(-10) * 1 x 10^3)
[HCl] > 3.316 x 10^(-6) M
Therefore, to ensure a significant precipitation of BaSO4, the initial HCl concentration should not exceed approximately 3.3 x 10^(-6) M. This range is well within the specified concentration of 0.01-0.05 M, demonstrating why the solution from which BaSO4 is precipitated cannot exceed this concentration.