QUANTITATIVE ANALYSIS

QUANTITATIVE ANALYSIS Chemistry 315, Section 501Third Homework Exam

March 27, 2014 (Due April 1, 2014) Cell Number _________

Please respond to the following questions

1. (25 points)

a.) (6 points) What is wave-particle duality? How is the concept used in spectrophotometry?

Wave particle duality has to do with the fact that light has both wave and particle-like properties. For example, electrons undergo diffraction that can interfere with each other as waves, but they also act as point-like masses. The theory of quantum mechanics is an attempt to explain these apparently contradictory properties exhibited by matter. In a dual sit experiment, light acts like a wave, because it can leave an interference pattern, which is what one would expect from a wave and not a particle. There are also many situations where light can act as a particle. For example when an electrons position is measured, a single point is found. The Photoelectric effect and the De Broglie hypothesis confirmed both the particle and the wave-like nature of light.

This concept leads us to the link between light attenuation and the concentration of particles its passing through, which is a foundation of spectrophotometry. Transitions between energy levels lead to absorption or emission of photons that correspond to the energy level difference. Spectrophotometry uses light to determine the concentration of chemicals. The absorbance, A,of a solution is a measure of how much light is absorbed by the solution. The particle nature of light allows the spectrophotometer to detect the light as photons are detected by a photomultiplier after passing through the analyte.

b.) (6 points) What is molar absorptivity? How is the concept used in spectrophotometry?

Molar absorptivity is the intensity of the analyte-photon interaction at a given wavelength. This can be used to calculate the concentrations of unknown solutions by combining molar absorptivity data gathered from standard solutions on a calibration curve.

In spectrophotometry, a spectrophotometer can be used to measure absorbency, which is used with the Beer-Lambert law to determine the concentration of an analyte. The solutions of known concentration are used to find the molar absorptivity by finding the slope of the line of best fit curve. If you test solutions of known concentrations, then you can compare the absorbances to solutions of unknown concentrations on a graph to find the concentration.

A=absorptivityb= the distance that the light travels through the solution(symbol)= molar absorptivityc=concentration of species (mol/L)

c.) (6 points) What does quantization of excitation energy mean? What role does the concept play in spectrophotometry? How does the concept of selection rules and quantum numbers play a role in spectrophotometry?

When an electron moves to a higher energy level, it absorbs energy. When an electron moves to a lower energy level, it emits energy. The quantization of excitation energy is the idea that energy can only be of specific values, or quantities to be absorbed or emitted by the electron, so electrons in orbit remain in a specific orbit unless provided with the amount of excitation energy needed to move them to the next specific orbital. The concept affects spectrophotometry because by this rule light only travels in packets of energy called photons, of specific energy amounts. It also links energy and wavelength of light, which play direct roles of spectrophotometry.

The energy that states that an electron occupies are quantized. That is, they exist in discrete units of energy. Their excitation energies give molecules their own molecular fingerprints, since each particle will have a unique set of energy levels. In spectrophotometry, this means different molecules will only absorb certain energy levels of light, which is useful for identification.

In spectrophotometry, quantum numbers describe specifically the energies of electrons in atoms, but other possibilities include angular momentum and spin. Selection rules provide constraints for an electron system to move from energy state to energy state via vibrational transitions.

d.) (6 points) What is the Beer-Lambert Law? Define all symbols used. What is its relevance to spectrophotometry?

A=absorptivityb= the distance that the light travels through the solution(symbol)= molar absorptivityc=concentration of species (mol/L)

2. 25 points)

a) (13 points) Describe the layout of a spectrophotometric system. What does each component do and give a conceptual account as to how it is used in chemical analysis?.

b.) (12 points). Give a conceptual description of the strategy that is used to employ spectrophotometry for chemical analysis.

First the sample must be dissolved in a solvent so the light can be passed through the sample while still interacting with it. A dilute sample must be used in order to obtain accurate results. Then the spectrophotometric system must record the initial intensity of the light going through a blank, which will be used in recording absorbance later. Next, a group of known concentration standards must be used to find the molar absorptivity of the solute that you want to measure the unknown concentration of. A standard curve is generated plotting these standards absorbance to their concentrations. The best fit line is used to calculate the slope of the equation (Beers law), which is the mentioned molar absorptivity of the compound at a certain length b (which is usually 1 cm). Once the molar absorptivity is found, the absorbance of the unknown is then measures to calculate the concentration of the sample using Beers Law, A=b

3.) (50 points) A sample of sunscreen was being analyzed for the concentration of oxybenzone using the spectrophotometric method. To set up the analysis, some initial measurements were made. First, a beam of 294 nm photons was send through a 1.25 cm long cuvette containing a solution of the sunscreen without the oxybenzone. The intensity of the beam passing through the cuvette was measured to be 2.52 x 106 photons per second.

Then, a second measurement was carried out using standard sample of sunscreen containing oxybenzone at a known concentration of 2.19 x 10-5 M. The intensity of the photon beam passing through this sample was measured to be 3.48 x 103 photons per second.

Finally, a third measurement was made on a sample of sunscreen containing an unknown concentration of oxybenzone. The photon beam intensity after passing through this sample was measured to be 2.82 x 104 photons per second.

a.) (10 points) Calculate the transmittance of the standard sample.

b.) (10 points) Calculate the absorbance of the standard sample.

c.) (10 points) Calculate the molar absorptivity of the oxybenzone

d.) (20 points) Calculate the concentration of the oxybenzone in the unknown sample of sunscreen. 1

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