Will AgCl precipitate out when equal amounts of 4.0 × 10-5M AgNO3 and 1.0 × 10-5M NaCl are mixed? (Ksp for AgCl = 1.8 × 10-10)
Qsp = (Ag^+)(Cl^-) = (4E-5)(1E-5) = 4E-10
Ksp = 1.8E-10
If Qsp > Ksp yes
If Qsp < Ksp no
THANK U BOB!!
To determine if AgCl will precipitate out when equal amounts of AgNO3 and NaCl are mixed, we need to compare the concentrations of Ag+ and Cl- ions with the solubility product constant (Ksp) for AgCl.
The balanced equation for the dissociation of AgCl is:
AgCl(s) ⇌ Ag+(aq) + Cl-(aq)
From the given concentrations of AgNO3 and NaCl, we can assume that both Na+ and NO3- ions do not contribute to the formation of AgCl precipitate.
The initial concentrations of Ag+ and Cl- ions are:
[Ag+] = 4.0 × 10^-5 M
[Cl-] = 1.0 × 10^-5 M
Since AgCl is a 1:1 electrolyte, the ionic concentrations after dissociation and equilibrium would also be equal to the given initial concentrations.
Using the solubility product expression:
Ksp = [Ag+][Cl-]
Substituting the values:
Ksp = (4.0 × 10^-5 M)(1.0 × 10^-5 M)
Calculating the value:
Ksp = 4.0 × 10^-10
The Ksp value for AgCl is 1.8 × 10^-10, which is less than the calculated Ksp. This means that the product of the concentrations of Ag+ and Cl- ions is greater than the solubility product constant (Ksp). Therefore, AgCl will precipitate out when equal amounts of 4.0 × 10^-5M AgNO3 and 1.0 × 10^-5M NaCl are mixed.
To determine if AgCl will precipitate out when equal amounts of AgNO3 and NaCl are mixed, we need to compare the product of the concentrations of Ag+ and Cl- ions to the solubility product constant (Ksp) for AgCl.
The balanced equation for the dissociation of AgCl in water is:
AgCl ⇌ Ag+ + Cl-
According to this equation, for every AgCl that dissolves, one Ag+ and one Cl- ion are formed. We can assume that the initial concentrations of Ag+ and Cl- ions in the solution are zero.
Let's denote the concentration of the Ag+ and Cl- ions that will form from the dissolving of AgCl as [Ag+] and [Cl-], respectively.
Since equal amounts of AgNO3 and NaCl are mixed, the initial concentrations of Ag+ and Cl- ions in the solution will be equal. Let's denote their initial concentrations as [Ag+]0 and [Cl-]0.
After mixing, the concentrations of Ag+ and Cl- ions will increase due to the dissociation of AgCl. Since one Ag+ and one Cl- ion are formed from one AgCl, the change in concentrations will be equal.
Therefore, after mixing, the concentrations of Ag+ and Cl- ions will be [Ag+]0 + [Ag+] and [Cl-]0 + [Cl-], respectively.
Now, let's substitute the concentrations of Ag+ and Cl- ions into the Ksp expression for AgCl:
Ksp = [Ag+][Cl-] = ( [Ag+]0 + [Ag+] ) ( [Cl-]0 + [Cl-] )
Since [Ag+] and [Cl-] increase by the same amount, we can simplify the expression:
Ksp = ( [Ag+]0 + x ) ( [Cl-]0 + x )
Given that [Ag+]0 = [Cl-]0 and x represents the increase in concentration of Ag+ and Cl- ions, we can write:
Ksp = ( [Ag+]0 + x ) ( [Ag+]0 + x )
Now, we can substitute the given concentrations and the Ksp value into the equation and solve for x:
1.8 × 10^-10 = (4.0 × 10^-5 + x) (1.0 × 10^-5 + x)
Solving this equation will give us the value of x, which represents the increase in concentration of Ag+ and Cl- ions. If x is greater than zero, it means that AgCl will precipitate out. If x is zero or negative, it means that AgCl will not precipitate out.
By solving the equation, we find that x is approximately -1.2 × 10^-5. Since x is negative, it means that there is no increase in concentration of Ag+ and Cl- ions, and therefore AgCl will not precipitate out.
Therefore, AgCl will not precipitate out when equal amounts of 4.0 × 10^-5M AgNO3 and 1.0 × 10^-5M NaCl are mixed.