Many compounds absorb light in the visible or ultraviolet portion of the electromagnetic spectrum. Beer's law governs the amount of radiation absorbed and indicates that absorbance is directly proportional to concentration. Thus, as the concentration of a compound dissolved in a given solvent increases, the absorbance of the solution should also increase proportionally. Chemists take advantage of this relationship to determine the concentration of unknown solutions. This first requires absorbance data on a series of solutions of known concentration called "standard" solutions. The absorbance and concentration data is then plotted in a "calibration curve" to establish their mathematical relationship. The concentration of the unknown sample can be determined by measuring its absorbance.

Construct a calibration plot of absorbance on the y-axis and concentration on the x-axis for the standard solutions. The data points should fall along a reasonably straight line. Two data points represent the absolute minimum, and more is better.

Draw a "best-fit" straight line through the data points and extend the line to intersect the y-axis. Choose two random points, not data points, on the line and determine their x and y coordinates. Label these coordinates as (x1,y1) and (x2,y2).

Calculate the slope, m, of the line according to the formula m = (y1 - y2) / (x1 - x2). Determine the y-intercept, abbreviated b, by noting the y-value where the line crosses the y-axis. For example, for two random points on the line at coordinates (0.050, 0.105) and (0.525, 0.315), the slope is given by

m = (0.105 - 0.315) / (0.050 - 0.525) = 0.440.

And if the line crosses the y-axis at 0.08, then this value represents the y-intercept.

Write the formula of the line of the calibration plot in the form y = mx + b. Continuing the example from Step 3, the equation would be y = 0.440x + 0.080. This represents the equation of the calibration curve.

Substitute the absorbance of the solution of unknown concentration into the equation determined in Step 4 as y and solve for x, where x represents concentration. If, for example, an unknown solution exhibited an absorbance of 0.330, using the equation determined in Step 4 would yield:

x = (y - 0.080) / 0.440 = (0.330 - 0.080) / 0.440 = 0.568 moles per litre.

#### Tip

Graphing data and determining the equation of the best-fit line is greatly facilitated by using the graphing features of Microsoft Excel or a similar program. See Resources for a tutorial on graphing in Excel. Although Beer's law states that absorbance and concentration are directly proportional, experimentally this is only true over narrow concentration ranges and in dilute solutions. Thus, standard solutions that range in concentration from, for example, 0.010 to 0.100 moles per litre will exhibit linearity. A concentration range of 0.010 to 1.00 moles per litre, however, will probably not.

#### Tips and warnings

- Graphing data and determining the equation of the best-fit line is greatly facilitated by using the graphing features of Microsoft Excel or a similar program. See Resources for a tutorial on graphing in Excel.
- Although Beer's law states that absorbance and concentration are directly proportional, experimentally this is only true over narrow concentration ranges and in dilute solutions. Thus, standard solutions that range in concentration from, for example, 0.010 to 0.100 moles per litre will exhibit linearity. A concentration range of 0.010 to 1.00 moles per litre, however, will probably not.

### Things you need

- Calculator
- Graph paper
- Ruler

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