what is the value of Kc if PbCl(s)=1.5g, [Pb2+]=1.6*10^-2 M and [Cl-] =3.2*10^-2 M at equilibrium? (The molar mass of PbCl(s) is 278 g/mol and its density is 5.85g/cm^3.)
Kc=[Pb2+]*[2*Cl-]^2
Kc=1.6E-2 * 4*(3.2E-2)^2
To find the value of Kc, we can use the formula for equilibrium constant expression using concentrations:
Kc = [Pb2+]^x * [Cl-]^y
Where x and y are the coefficients of Pb2+ and Cl- in the balanced chemical equation.
The balanced chemical equation for the dissolution of PbCl(s) in water is:
PbCl(s) ⇌ Pb2+(aq) + 2Cl-(aq)
From the equation, we see that the coefficient for Pb2+ is 1 and the coefficient for Cl- is 2.
Now, let's calculate the concentrations of Pb2+ and Cl-.
Given:
Mass of PbCl(s) = 1.5 g
Molar mass of PbCl(s) = 278 g/mol
Density of PbCl(s) = 5.85 g/cm^3
Step 1: Calculate the volume of PbCl(s)
Volume = mass / density = 1.5 g / 5.85 g/cm^3 = 0.2564 cm^3
Step 2: Convert the volume to liters
1 cm^3 = 1 mL = 1 x 10^-3 L
Volume = 0.2564 cm^3 x 1 x 10^-3 L/cm^3 = 2.564 x 10^-4 L
Step 3: Calculate the moles of PbCl(s)
Moles = mass / molar mass = 1.5 g / 278 g/mol = 5.395 x 10^-3 mol
Step 4: Calculate the concentrations of Pb2+ and Cl-
[Pb2+] = Moles / Volume = 5.395 x 10^-3 mol / 2.564 x 10^-4 L = 2.1047 x 10^-2 M
[Cl-] = 2 * [Pb2+] = 2 * 2.1047 x 10^-2 M = 4.2094 x 10^-2 M
Now, substitute the values into the equilibrium constant expression:
Kc = [Pb2+]^1 * [Cl-]^2
= (2.1047 x 10^-2)^1 * (4.2094 x 10^-2)^2
= 3.180 x 10^-5
Therefore, the value of Kc is 3.180 x 10^-5.