When describing chemical compounds, scientists rely on their chemical and physical properties. In lab, we might observe that a metal reacts violently with water, that a reactant is liquid at room temperature, or that a powder is yellow. Chemical and physical properties can be used qualitatively to identify a material or to predict its behavior, or quantitatively to determine how much of that material is present in a solution. In this lab, we will develop a scheme to determine the concentration of copper sulfate in aqueous solution using spectrophotometry.

To start, we will consider light and its interaction with matter. Chemicals exhibit a diverse range of colors, especially when they contain transition metal ions. In order for a compound to have color, it must absorb visible light. Visible light consists of electromagnetic radiation with wavelengths ranging from approximately 400 nm to 700 nm, a small section of the electromagnetic radiation spectrum shown below.

Light is characterized by its frequency ( νν size 12{ν} {}), the number of times the crest of the wave passes some point in space per second, or by its wavelength ( λλ size 12{λ} {}), the distance between two successive crests. These two quantities are related by the speed of light, a fundamental constant: λν=c=3×108m/sλν=c=3×108m/s size 12{"λν"=c=3 times "10" rSup { size 8{8} } "m/s"} {}. Planck related the frequency of light to its energy (E) according to E=hνE=hν size 12{E="hν"} {}, where h is Planck's constant, h=6.626×10−34J/sh=6.626×10−34J/s size 12{h=6 "." "626" times "10" rSup { size 8{ - "34"} } "J/s"} {}.

A compound will absorb light when the radiation posesses the energy needed to move an electron from its lowest energy (ground) state to some excited state. The particular energies of radiation that a substance absorbs dictate the colors that it exhibits. Conversely the color of a compound can help us to determine its electronic configuration.

White light contains all wavelengths in this visible region. When a transparent sample (like most aqueous solutions) absorbs visible light, the color we perceive is the sum of the remaining colors that are transmitted by the object and strike our eyes. If an object absorbs all wavelengths of visible light, none reaches our eyes, and it appears black. If it absorbs no visible light, it will look white or colorless. If it absorbs all but orange, the material will appear orange. We also perceive an orange color when visible light of all colors except blue strikes our eyes. Orange and blue are complementary colors; the removal of blue from white light makes the light look orange, and vice versa. Thus, an object has a particular color for one of two reasons: It transmits light of only that color or it absorbs light of the complementary color.

Figure 1

Complementary colors can be determined using an artist's color wheel. The wheel shows the colors of the visible spectrum, from red to violet. Complementary colors, such as orange and blue, appear as wedges opposite each other on the wheel.

With our eye, we can make qualitative judgments about the color(s) of light a sample absorbs. However, given a red solution of [Ti(H2O)6]3+[Ti(H2O)6]3+ size 12{ \[ "Ti" \( H rSub { size 8{2} } O \) rSub { size 8{6} } \] rSup { size 8{3+{}} } } {} we can not determine if it absorbs green light or if it absorbs all colors of light but red. To quantitatively determine the amount of light absorbed by a sample as a function of wavelength, we will measure its absorption spectrum using a UV-visible spectrophotometer. Typical absorption spectra of aqueous [Ti(H2O)6]3+[Ti(H2O)6]3+ size 12{ \[ "Ti" \( H rSub { size 8{2} } O \) rSub { size 8{6} } \] rSup { size 8{3+{}} } } {} solutions are shown below.

Notice the absorption maximum is at 490 nm. Because the sample absorbs more strongly in the green and yellow regions of the visible spectrum, it appears red-violet. Measuring the absorption spectrum of a second, more dilute solution demonstrates that the spectrum changes as a function of the concentration of the solution. To understand how to use the absorption spectrum as a quantitative tool for chemical analysis, read on!

Spectrophotmetric Basics

The essential components of a spectrophotometer consist of a radiation source, a wavelength selector (monochromator), a photodetector and read-out device.

Figure 2

The incident light from a tungsten (visible light source) or deuterium (UV light source) lamp is focused by a lens and passes through an entrance slit. By passing the beam through the monochromator (either a prism or a diffraction grating) it is separated into monochromatic (i.e., one-color or single-wavelength) light. One particular wavelength of monochromatic light is selected and allowed to pass through the exit slit into the sample. Light transmitted through the sample is detected by a photodetector which converts the signal to an electrical current which is measured by a galvanometer and sent to a recording device, typically a computer.

The measurement of transmittance (T) is made by determining the ratio of the intensity of incident ( I0I0 size 12{I rSub { size 8{0} } } {}) and transmitted (I) light passing through pure solvent and sample solutions as a function of wavelength. [Note: The percent transmittance (%T) is obtained by multiplication of T by 100.] The logarithm of the reciprocal of the transmittance is called the absorbance (A),

A = log (1 / T)

Care must be taken when small values of transmittance are being measured as stray light from either the room or scattering within the instrument can cause large errors in your readings!

Extracting Quantitative Information

The Beer-Lambert law relates the amount of light being absorbed to the concentration of the substance absorbing the light and the pathlength through which the light passes:

A = εbc . A = εbc . size 12{A="εbc" "." } {}

In this equation, the measured absorbance (A) is related to the molar absorptivity constant ( εε size 12{ε} {}), the path length (b), and the molar concentration (c) of the absorbing. The concentration is directly proportional to absorbance.

The single largest application of the spectrophotometer is for quantitative analysis. The prerequisite for such analysis is a known absorption spectrum of the compound under investigation. Of particular importance is the maximum absorption (at λmaxλmax size 12{λ rSub { size 8{"max"} } } {}) [Why choose the maximum? Could the choice alter the precision of our experiment? the accuracy?], which can be easily obtained by plotting absorbance vs. wavelength at a fixed concentration. Next, a series of solutions of known concentration are prepared and their absorbance is measured at λmaxλmax size 12{λ rSub { size 8{"max"} } } {}. Plotting absorbance vs. concentration, a calibration curve can be determined and fit using linear regression (least-squares fit). An unknown concentration can be deduced by measuring absorbance at the absorption maximum and comparing it to the standard curve. Caution: The Beer-Lambert Law is only obeyed (the standard curve is linear) for reasonably dilute solutions. Only those points in the linear range of the standard curve may be used for accurate concentration determination.

Typical results are shown for the absorbance of [Ti(H2O)6]3+[Ti(H2O)6]3+ size 12{ \[ "Ti" \( H rSub { size 8{2} } O \) rSub { size 8{6} } \] rSup { size 8{3+{}} } } {} measured at 490 nm.

Table 1

Concentration (mg/mL)	%Transmittance	Absorbance
0	100.	0
1	50.0	0.301
2	25.0	0.602
3	12.5	0.903

Figure 3

Over the studied range the solutions obey Beer's Law. If a solution has a measured absorbance of 0.450, we can calculate its concentration to be 1.5 mg/mL.

Plot the concentration as a function of absorbance for your six solutions. Perform a linear regression analysis and determine the equation of a best-fit line.

EXCEL INSTRUCTIONS: