Biol 1440, Principles of Biology I

Data Collection
Estimating Concentration form Absorbance

Lambert-Beer Law
Lambert-Beer Law is used to determine concentration [c] from Absorbance [A], if the molar extinction coefficient [e] of a compound and the distance light passes through the solution are known.  The formula is:

A = ecl

Thus,  concentration can be calculated by:  c=A/el

Example: the molar extinction coefficient for betacyanin is approximately 38,000 L/mole-cm, the path length for the Spectronic 20 spectrophotometer is 1.2cm.  If the Absorbance of beet betacyanin extract is 1.0, then

c = 1.0 A /38,000 L/mole-cm X 1.2cm
c = 1.0 A /45,600 L/mole (use this value for your data)
c = 2.193 x10 e
-5
      or 22 microM (
mM)

ShortCut to finding betacyanin concentration in mM
c = A530/0.0456

For any given solute, the amount of light absorbed is proportional to the concentration of the solute in the solution.

stdcurv1.jpg (10866 bytes)

[ ] = Concentration  Units: 1 mole/l = 1M, molar

Making solutions of known concentration using the mass balance principle
In order to construct a standard curve, it is necessary to make a series of reference solutions of known concentration.  Usually such solutions are prepared from a stock solution using the formula:

C1V1 = C2 V2

where,
C1 = the concentration of the stock solution          V1 = the volume of stock solution used
C2 = final concentration of diluted stock solution    V2 = final volume of diluted stock solution

If one knows the stock concentration
C1 and the final concentration of diluted stock solution C2 and the final volume of diluted stock solution V2, then one solves for V1Remember that   V2 is greater than V1, so to bring V1 to the final volume = V2, a volume of solution usually distilled water, dH2O,  must be added to dilute the stock solution to a lower concentration. 

Thus, V2 = V1 + VdH20.  The VdH20 can be calculated by subtraction,

V2 -V1 = VdH2O

Try these problems to test your understanding of mass-balance [Review Mass Balance]

Constructing a table of dilutions
Constructing a table of dilutions for all volumes and concentrations will help in preparing your standard curve. Try this technique to form the following solutions. 

Example
The stock solution is 80% ethanol, EtOH (C1), the diluted stock solutions are 50% (C2) and 10
% (C2) EtOH, each has a final volume (V2)of 10 mL. 

Table of Dilution for a 100mM betacyanin  stock solution

C1
stock conc.
ethanol

V1
vol. of stock to add

C2
desired conc. for expt.

V2
desired final vol. for expt

VdH2O
vol. of water to add for V2.

80%

 

40%

10 mL

 

80%

 

10%

10 mL

 

To calculate V1 and VdH2O to make 50% EtOH.

1. Solve for V1

V1=C2/C1*V2, thus V1= 40% / 80% * 10mL

V1= 0.5 * 10mL = 5mL of 80% EtOH (C1)

2. Solve for VdH2O to adjust the final volume to 10mL by subtracting: V2-V1 = VdH2O.

10mL - 5mL = 5mL dH2O.

Thus, a 40% EtOH solution can be made by adding  5mL of 80% EtOH to 5mL of distilled water. Does this make sense? Sure a 40% solution is half, or 0.5, less concentrated than a 80% solution, so combining equal volumes of 80% EtOH  and dH2O should result in a solution half as concentrated.

To calculate V1 and VdH2O to 10mM betacyanin .

1. Solve for V1

V1=C2/C1*V2, thus V1= 10% / 80% * 10mL

V1= 0.125 * 10mL = 1.25mL of C1

2. Solve for VdH2O to adjust the final volume to 10mL by subtracting: V2-V1 = VdH2O.

10mL - 1.25mL = 8.75mL dH2O.

Thus, a 105 EtOH solution can be made by adding 1.25mL of 80% EtOH to 8.75mL of distilled water.

Constructing a dilution table of all volumes and concentrations will help in preparing your ethanol concentrations.    

C1
stock conc.
EtOH

V1
vol. of stock to add

C2
desired conc.
EtOH 

V2
desired final vol. for expt.
VdH2O
vol. of water to add for
V2.