The metal ion M2+ in ammonia, NH3 forms the complex ion M(NH3)62+ (Kf = 5.1x108). Calculate the M2+ concentration when the equilibrium concentrations of NH3 and M(NH3)62+ are 0.057 and 0.45 M respectively.
See your post below with the MX and NaCN
To solve this problem, we can use the concept of equilibrium constant (Kf) and the equation for the formation of the complex ion M(NH3)62+:
M2+ + 6NH3 ⇌ M(NH3)62+
We are given the equilibrium concentrations of NH3 and M(NH3)62+:
[ NH3 ] = 0.057 M
[ M(NH3)62+ ] = 0.45 M
And the equilibrium constant (Kf) is given as Kf = 5.1x10^8.
To find the concentration of M2+ ( [ M2+ ] ), we can use an ICE (Initial-Change-Equilibrium) table.
Step 1: Write the balanced equation:
M2+ + 6NH3 ⇌ M(NH3)62+
Step 2: Set up the ICE table:
M2+ + 6NH3 ⇌ M(NH3)62+
I: 0M 0.057M
C: -x -6x
E: x 0.057 - 6x
Step 3: Use the relationship between the equilibrium concentrations and the equilibrium constant to set up an expression:
Kf = [ M(NH3)62+ ] / ( [ M2+ ] * [ NH3 ]^6 )
Substituting the given values:
5.1x10^8 = 0.45 / ( [ M2+ ] * ( 0.057^6 ) )
Step 4: Solve for [ M2+ ]:
Cross-multiplying the equation, we get:
5.1x10^8 * [ M2+ ] * ( 0.057^6 ) = 0.45
Simplifying:
[ M2+ ] * ( 0.057^6 ) = 0.45 / ( 5.1x10^8 )
[ M2+ ] = (0.45 / ( 5.1x10^8 )) / ( 0.057^6 )
Calculating the value:
[ M2+ ] = 2.679x10^-5 M
Therefore, the concentration of M2+ is 2.679x10^-5 M when the equilibrium concentrations of NH3 and M(NH3)62+ are 0.057 and 0.45 M, respectively.
To calculate the M2+ concentration, we can use the equilibrium constant expression. Let's assume x is the concentration of M2+.
The equilibrium constant expression for the formation of complex ion M(NH3)62+ is given as:
Kf = [M(NH3)62+] / ([M2+][NH3]^6)
Plugging in the given equilibrium concentrations:
Kf = 0.45 / (x * (0.057)^6)
Let's rearrange the equation to solve for x (M2+ concentration):
x = 0.45 / (Kf * (0.057)^6)
Now we can substitute the given values:
x = 0.45 / (5.1x10^8 * (0.057)^6)
Calculating this equation will give us the value of x, which represents the concentration of M2+.