A student proposes to use visible spectroscopy to measure the kinetics of the permanganate/oxalic acid reaction. The initial permanganate solution was very dark. For a 1 cm sample cell, the absorbance A = 2,500[MnO4]. As a practical rule of thumb, Beer's law is only accurate below an absorbance value of A = 1.00. This limits the initial permanganate concentration that can be used.
A: What is the maximum permanganate concentration that can be used and still have A = 1.00?
B: If the detection limit for the spectrometer is A = 0.01, what is the minimum permanganate concentration that can be detected?
C: The rate law for the reaction was determined to be:
[MnO4-]0/t = 0.052[mnO4]0^-1.29 * [H2C2O4]0^0.76
If [H2C2O4]0 = 0.30 mol/L and [MnO4] is the maximum it can be for visible spectroscopy, how long would it take for the the permanganate to be used up? Remember the rate law given above was for the average rate for the complete conversion of MnO4- to Mn2+.
A. If A = 2,500(MnO4^-) and you want A to be 1.00, Substitute 1.00 into the above and solve for (MnO4^-).
B. Substitute 0.01 for A and solve for (MnO4^-)
I don't get c.
A: To determine the maximum permanganate concentration that can be used and still have A = 1.00, we need to consider Beer's law. Beer's law states that the absorbance of a solution is proportional to the concentration of the absorbing species and the path length of the sample cell.
In this case, the absorbance of the permanganate solution is A = 2,500[MnO4]. Since we have a 1 cm sample cell, we can set up the equation as A = εbc, where ε is the molar absorptivity (extinction coefficient), b is the path length (1 cm), and c is the concentration of the absorbing species ([MnO4]).
Substituting the values into the equation, we have 2,500 = ε * 1 * [MnO4].
To find the maximum permanganate concentration, we need to solve for [MnO4] when A = 1.00. Rearranging the equation, we have ε * 1 * [MnO4] = 1.00.
Since A = εbc, we can rewrite the equation as ε * 1 * [MnO4] = ε * 1 * 1.00.
Cancelling out ε and 1 on both sides of the equation, we get [MnO4] = 1.00.
Therefore, the maximum permanganate concentration that can be used and still have A = 1.00 is 1.00.
B: To determine the minimum permanganate concentration that can be detected when the detection limit for the spectrometer is A = 0.01, we can use the same equation A = εbc.
In this case, A = 0.01 and the path length b is still 1 cm. We want to find the minimum concentration [MnO4] that gives an absorbance of 0.01.
Using the equation A = εbc, we have 0.01 = ε * 1 * [MnO4].
Rearranging the equation, we get ε * 1 * [MnO4] = 0.01. Dividing both sides by ε and 1, we obtain [MnO4] = 0.01/ε.
Therefore, the minimum permanganate concentration that can be detected when the detection limit is A = 0.01 is 0.01/ε.
C: The rate law for the reaction is given as:
[MnO4-]₀/t = 0.052[MnO4]₀⁻¹.²⁹ * [H2C2O4]₀⁰.⁷⁶.
To find out how long it would take for the permanganate to be used up, we need to determine the reaction time (t) when the concentration of [MnO4] reaches zero.
Given that [H2C2O4]₀ = 0.30 mol/L as constant, we want to find the time (t) required for the complete conversion of [MnO4] from its initial concentration to zero when [MnO4]₀ = maximum value allowed for visible spectroscopy.
First, we need to determine the value of [MnO4]₀, which is the maximum permanganate concentration that can be used from part A (maximum permanganate concentration = 1.00).
Substituting the values into the rate law equation, we have:
0/t = 0.052 * (1.00)⁻¹.²⁹ * (0.30)⁰.⁷⁶.
Simplifying this equation, we get:
0/t = 0.052 * 1.00 * (0.30)⁰.⁷⁶.
0/t = 0.052 * (0.30)⁰.⁷⁶.
The left side of the equation is zero since the concentration of [MnO4] reaches zero. Therefore, the equation becomes:
0 = 0.052 * (0.30)⁰.⁷⁶.
To solve for t, we need to isolate the variable. Dividing both sides of the equation by 0.052 * (0.30)⁰.⁷⁶, we get:
0/(0.052 * (0.30)⁰.⁷⁶) = 1.
Since any number divided by zero is undefined, we cannot determine an exact time for complete conversion.
However, since the reaction is dependent on the concentration of [MnO4], the time required for the permanganate to be used up would be significantly longer as [MnO4] approaches zero.
Therefore, in the given scenario, it would take a long time for the permanganate to be completely used up.