Deriving Chem Beer's Law's Equation
By comparing the absorbance of each trial solution, Aeq, to the absorbance of the standard solution, Astd, [FeNCS2+]eq can be determined. Two Beer’s Law equations can be written, one for the trial (Aeq = ε[FeNCS2+]eql), one for the standard (Astd = ε[FeNCS2+]stdl).
Set these two equations equal to each other to derive equation (2).
Note : the "l" is a special symbol as well
The derived equation looks like this : [FeNCS2+]eq = Aeq / Astd *[FeNCS2+]std
I'm having trouble deriving it myself? Any tips or help would greatly be appreciated!
The hint tells you how to do it. Set the two equations equal to each other and solve for [FeNCS2+]eq.
I don't understand how its Aeq / Astd * [FeNCS2+]std
What am I setting equal exactly?
ε[FeNCS2+]eql)/Aeq = ε[FeNCS2+]stdl/Astd ?
solve for the epsilon and then plug them in.
To derive equation (2) from the two Beer's Law equations, let's start by writing them down:
Equation 1: Aeq = ε[FeNCS2+]eql
Equation 2: Astd = ε[FeNCS2+]stdl
Now, we want to set these two equations equal to each other:
Aeq = Astd
Substituting the values from the Beer's Law equations, we have:
ε[FeNCS2+]eql = ε[FeNCS2+]stdl
Since we are trying to derive the equation [FeNCS2+]eq = Aeq / Astd * [FeNCS2+]std, we need to manipulate the equation further.
First, divide both sides of the equation by ε and [FeNCS2+]std:
[FeNCS2+]eql / [FeNCS2+]std = 1
Now, let's simplify the left side of the equation by cancelling out [FeNCS2+]l on both sides:
eql / std = 1
Finally, rearrange the equation to solve for [FeNCS2+]eq:
[FeNCS2+]eq = eql / std
It is important to note that the "l" in the equations represents the path length of the cuvette used for measuring absorbance. This value is usually kept constant for a particular experiment. Hence, when comparing different absorbance values, the path length cancels out, and we can ignore it in our final equation.
Therefore, the derived equation becomes:
[FeNCS2+]eq = Aeq / Astd * [FeNCS2+]std
This equation allows us to determine the concentration of [FeNCS2+]eq based on the absorbances of the trial solution (Aeq) and the standard solution (Astd).