Analysis: Solving problems which involve in standard addition method formula




Question
A chemist determined the levels of iron in dry leaves collected from a plant near her homestead, she weighed 15 grams of the leaves and dissolved them in a mixture of acids, filtered the resulting solution in a 250mlvolumeric flask. She pipetted 10mls of the solution to a 50ml volumetric flask and topped it to the mark using deionized water. This solution gave absorbance of 0.56. She pipetted another 10mls into another 50ml flask, added 4mls of 3 x 10^-4 M iron solution and made it to the mark with deionized water. This solution gave absorbance of 0.72.
(i)                  Calculate the concentration of iron in prepared leaf solution?
(ii)                Calculate the concentration of iron in the leaves in mg/g of the leaves?
This question needs the application of the formula of “standard addition method’’. The formula is given by:
SSVf/ ((Cx Vx) + (CsVs)) = SVf/ (CxVx);
Where:
SS- represent absorbance of the spiked sample
S-Represent absorbance of unspiked sample
Vf-represent final volume of either spiked sample or unspiked sample
Cx- represents concentration of the sample
Vx- represents the volume of the sample 
Cs-represent the concentration of the standard
Vs-represent the volume of the standard
NB: spiked sample is a sample in which the standard has been added to while unspiked one is that without addition of the standard.
Solutions
(i)
The following are provided:
SS=0.72
S=0.56
Vf=50ml
Vx= 10ml
Vs= 4mls
Cs= 3 x 10^-4
NB: moles always confuse most students, don’t do this:
1000mls = 3 X 10^-4
3mls =?
The molarity in this case doesn’t change.
Since the information provided is enough to get the concentration of the species under investigation. Substitution in the above equation will give the answer as shown below:
0.72 X 50/((Cx X 10ml) + (3 X 10^-4 X 4ml)) = 0.56 X 50/(Cx X 10ml)
36(Cx X 10ml) =28((Cx X 10) + (3 X 10^-4 X 4ml))
 360Cx= ((280Cx +28(0.0012))
 360Cx = 280Cx +0.0336
Collecting like terms;
360CX – 280CX = 0.0336
80Cx = 0.0336
Cx= (0.0336/80)
=0.00042 moles
(ii)
The mass of iron in 10mls of sample will be;
R.A.M of iron = 55.845g
But to get number of moles of substance is given by:
Given mass/R.A.M of that substance
Mass of iron in 10ml = (0.00042 X 55.845)g
= 0.02345g
But answer is needed in miligrams, therefore converting it gives:
(0.02345g X 100)
= 2.345 miligrams
Now concentration of iron in 250ml of prepared solution gives:
10ml = 2.345mg
250ml=?
(250 X 2.345mg)/10
=586.25mg
In 15 grams of leaves which were weighed, this become: Divide the answer by 15 grams;
(586.25mg/15g)
= 39.08333mg/g

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