For a reaction involving ionic reactants described by the mechanism given by
A + B <===> (A-B)* ===> P
log k= log k1Kc + 1.0332 ZaZb I^1/2 where I is the ionic strength of the solution. Given log k1Kc = -2.861
S2O8^2- (aq) + 2I^- (aq) =======> 2SO4^2- (aq) + l2 (aq)
Determine k( L.mol/s) for a reaction mixture containing C (KI) = 0.010 M and C (Na2S2O8) = 1.5 x 10^-4 M.
To determine k for the reaction, we first need to find the value of Kc, which is the equilibrium constant.
The given equation is:
S2O8^2- (aq) + 2I^- (aq) =======> 2SO4^2- (aq) + l2 (aq)
From the equation, we can see that the stoichiometric coefficients of S2O8^2- and I^- are both 1, while the stoichiometric coefficients of SO4^2- and I2 are both 2. Therefore, we can write the equilibrium expression as:
Kc = ([SO4^2-]^2 [I2]) / ([S2O8^2-] [I^-]^2)
Now, we can substitute the given concentrations into the equilibrium expression:
Kc = ([SO4^2-]^2 [I2]) / ([S2O8^2-] [I^-]^2)
= (2x)^2 (x) / ((1.5x10^-4) (0.010)^2)
= 4x^3 / 1.5x10^-6
Simplifying, we get:
Kc = 2.6667x10^12
Next, we can substitute the value of log k1Kc (which is -2.861) and the given equation for log k into the given equation:
log k = log k1Kc + 1.0332 ZaZb I^1/2
log k = -2.861 + 1.0332(1)(2) (0.5I^1/2)
log k = -2.861 + 2.0664 (0.5I^1/2)
Now, we need to calculate the value of I, the ionic strength of the solution. In this case, I can be calculated as the sum of the product of the square of the concentration of each ionic species multiplied by its charge:
I = (C(S2O8^2-)(2)^2) + (C(I^-)(1)^2) + (C(SO4^2-)(2)^2) + (C(I2)(2)^2)
= (1.5x10^-4)(2)^2 + (0.010)(1)^2 + (0)(2)^2 + (0)(2)^2
= 6x10^-4 + 0.01 + 0 + 0
= 6.01x10^-3
Substituting the value of I into the equation for log k:
log k = -2.861 + 2.0664 (0.5(6.01x10^-3)^1/2)
log k = -2.861 + 2.0664 (0.5(2.447x10^-2)^1/2)
log k = -2.861 + 2.0664 (0.5(4.947x10^-1)^1/2)
log k = -2.861 + 2.0664 (0.5(0.7016)^1/2)
log k = -2.861 + 2.0664 (0.5(0.8370)^1/2)
log k = -2.861 + 2.0664 (0.5(0.9150))
log k = -2.861 + 2.0664 (0.5(0.4575))
log k = -2.861 + 2.0664 (0.2288)
log k = -2.861 + 0.4713
log k = -2.3897
Finally, we can find k by taking the antilog of -2.3897:
k = 10^(-2.3897)
k = 0.004215 L.mol/s
Therefore, the value of k for the reaction mixture is 0.004215 L.mol/s.
To determine the rate constant (k) for the given reaction mixture, we need to use the equation for the rate constant in terms of log k1Kc, ionic strength (I), and other values.
The equation given is:
log k = log k1Kc + 1.0332 ZaZb I^1/2
First, let's calculate the value of I (ionic strength) using the concentration of the ions present in the reaction mixture. The ionic strength for this reaction is given by the equation:
I = 1/2 (C1z1^2 + C2z2^2 + ... + Cnz^2)
Given:
C(KI) = 0.010 M
C(Na2S2O8) = 1.5 x 10^-4 M
For KI:
C1 = 0.010 M
z1 = charge of K+ = 1
For Na2S2O8:
C2 = 1.5 x 10^-4 M
z2 = charge of S2O8^2- = -2
Calculating ionic strength:
I = 1/2 (C1z1^2 + C2z2^2)
= 1/2 [(0.010 M)(1^2) + (1.5 x 10^-4 M)(-2)^2]
= 1/2 (0.010 + 6 x 10^-8)
= 0.01000003
Now, let's substitute the known values into the given equation:
log k = log k1Kc + 1.0332 ZaZb I^1/2
Given:
log k1Kc = -2.861
Za = charge of S2O8^2- = -2
Zb = charge of I^- = -1
I = 0.01000003
Substituting the values:
log k = -2.861 + 1.0332 (-2) (-1) (0.01000003)^1/2
Simplifying the equation:
log k = -2.861 + 0.02066696
= -2.84033304
To solve for k, we need to take the antilog (inverse logarithm) of both sides:
k = 10^(-2.84033304)
Using a calculator, the value of k is approximately 0.0058 L.mol/s.