Because of the changing color of the solution as the following reaction proceeds, the rate law can be determined by measuring the rate of disappearance of the permanganate ion (MnO4-). 2MnO4-(aq)+ 5H2C2O4(aq) + 6H+(aq) -> 2Mn2+(aq) + 10CO2(g) + 8H2O(l)
The following initial rate data was found for the reaction:
[MnO4] (M)= 2.0 x 10^-3
[H2C2O4] (M)= 2.0 x 10^-3
[H+] (M)= 1.0 x 10^-3
The reaction is second order for MnO4, first order for H2C2O4 and zero order for H+. This reaction could also be monitored by measuring the formation of CO2(g). Determine the initial rate of the reaction in terms of appearance of CO2(g) in M/sec given the same conditions as in experiment above.
some one help please!
To determine the initial rate of the reaction in terms of the appearance of CO2(g), we need to use the stoichiometry of the reaction.
From the balanced equation: 2MnO4-(aq) + 5H2C2O4(aq) + 6H+(aq) -> 2Mn2+(aq) + 10CO2(g) + 8H2O(l), we can see that for every 2 moles of MnO4- consumed, 10 moles of CO2 are produced.
Given the initial concentrations:
[MnO4] = 2.0 x 10^-3 M
[H2C2O4] = 2.0 x 10^-3 M
[H+] = 1.0 x 10^-3 M
Since the reaction is second order for MnO4, first order for H2C2O4, and zero order for H+, we can write the rate law as follows:
Rate = k[MnO4]^2[H2C2O4]^1[H+]^0
Now, let's substitute the initial concentrations into the rate law expression:
Rate = k(2.0 x 10^-3)^2(2.0 x 10^-3)^1(1.0 x 10^-3)^0
Rate = k(4.0 x 10^-6)(2.0 x 10^-3)
Rate = k(8.0 x 10^-9)
The rate constant (k) represents the specific rate of the reaction, which we do not have. Therefore, we cannot calculate the exact value for the initial rate in M/sec at the given conditions.
To determine the initial rate of the reaction in terms of the appearance of CO2(g), we need to use the rate law and the stoichiometry of the reaction.
Based on the given information, the reaction is second order for MnO4-, first order for H2C2O4, and zero order for H+:
rate = k[MnO4-]^2[H2C2O4]^1[H+]^0
Since the order of H+ is zero, it doesn't appear in the rate equation, so we can omit it. The rate law becomes:
rate = k[MnO4-]^2[H2C2O4]^1
Now, let's use the initial rate data provided to determine the value of the rate constant (k).
From the initial rate data, we have:
[MnO4-] (M) = 2.0 x 10^-3
[H2C2O4] (M) = 2.0 x 10^-3
Using these concentrations, and assuming the initial rate of the reaction is given in M/sec, we can substitute them into the rate law equation:
rate = k(2.0 x 10^-3)^2(2.0 x 10^-3)^1
Simplifying the equation:
rate = k(4.0 x 10^-6)(2.0 x 10^-3)
rate = 8.0 x 10^-9 k
Now, we can calculate the value of k using the rate data given:
Let's assume the initial rate of the reaction in terms of CO2(g) appearance is represented as [CO2]/Δt, where [CO2] is the concentration of CO2 and Δt is the time interval.
Given the initial rate of the reaction in terms of permanganate ion disappearance (MnO4-) is 2.0 x 10^-9 M/sec, we can set up the following stoichiometric conversion:
(2.0 x 10^-9 M/sec)(10 CO2/2 MnO4-) = [CO2]/Δt
Simplifying the equation:
(2.0 x 10^-9 M/sec)(5) = [CO2]/Δt
1.0 x 10^-8 M/sec = [CO2]/Δt
Therefore, the initial rate of the reaction in terms of the appearance of CO2(g) is 1.0 x 10^-8 M/sec.