The polarogram for 20ml solution that was 3.65 x 10^-3 M in cadmium (Cd2+) gave a wave for that ion with a diffusion current of 31.3microampere. Calculate the percentage change in concentration of the solution is the current in the limiting current region were allowed to continue for 5 minutes.
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-0.05%
To calculate the percentage change in concentration of the solution, we need to determine the value of the diffusion coefficient of the Cd2+ ion and use it to find the concentration change in the solution.
The diffusion current (Id) is given as 31.3 microampere, which is equivalent to 31.3 × 10^-6 A.
First, we need to calculate the diffusion coefficient (D) using the Nernst-Einstein equation:
Id = (2.69 × 10^5) × D × C × A
where:
- Id is the diffusion current (31.3 × 10^-6 A).
- D is the diffusion coefficient (to be determined).
- C is the concentration of the Cd2+ ion (3.65 × 10^-3 M).
- A is the area of the working electrode in cm^2 (assume 1 cm^2 for simplicity).
Substituting the given values into the equation, we can solve for D:
31.3 × 10^-6 A = (2.69 × 10^5) × D × (3.65 × 10^-3 M) × (1 cm^2)
D = (31.3 × 10^-6 A) / [(2.69 × 10^5) × (3.65 × 10^-3 M) × (1 cm^2)]
Now, we have the diffusion coefficient, D.
To calculate the concentration change (∆C) after 5 minutes of diffusion in the limiting current region, we can use Fick's second law of diffusion:
∆C = (2×D×t) / (L^2)
where:
- ∆C is the concentration change.
- D is the diffusion coefficient (calculated earlier).
- t is the time in seconds (5 minutes = 300 seconds).
- L is the length of the diffusion path (assume 0.1 cm for simplicity).
Substituting the values into the equation:
∆C = (2 × D × t) / (L^2)
= (2 × D × 300 s) / (0.1 cm)^2
Now we have the concentration change (∆C). To find the percentage change, we can use the formula:
Percentage Change = (∆C / initial concentration) × 100
Substituting the values into the equation:
Percentage Change = (∆C / (3.65 × 10^-3 M)) × 100
Now you can solve for the percentage change in concentration using the calculated values.