Exam #1 Name __________________________________ Instructions. This exam is worth 100 points. The points allocated to each section are indicated at the beginning of the section. Some sections allow a choice as to which questions are answered. For these sections, do not answer more parts than requested. If all parts are answered, consecutive questions will be graded beginning with the first part. In calculations, be sure to report your answer with the correct number of significant figures. Physical Constants and Conversion Factors velocity of light in a vacuum: 3.00x108 m/sec Planck's constant: 6.626x10-34 Joule-sec electron charge: 1.602x10-19 Coulomb 1 Joule = 1 Volt-Coulomb Avogadro's constant: 6.022x1023 atoms/mole 1 nm = 10-9 m 1 cm = 10-2 m 1 mm = 10-3 m 1 µm = 10-6 m Equations s = [3(yi-yG)2/(n-1)]½ yG = 3yi/n confidence interval = ts/n½ sr = [3(yi-y^i)2/(n-2)]½ y^i = mxi + b λν = c Gν = 1/λ E = hν T = P/P0 A = -log10(T) A = εbc ALOD = b + 3sr CLOD = 3sr/m CLOQ = 10sr/m nq = c / vq (q = medium) sin r = nλ/d - sin i sin i / sin r = n2 / n1
Chemistry 325
Instrumental Analysis
February 4, 2004
1. (40 points) Circle the correct answer for ten of the following: a. The precision of an analytical measurement (1) is described by calculating percent relative error. (2) is related to the width of the population distribution of the measurement. (3) is guaranteed to be high if the measurement also has high accuracy. (4) none of the above. b. The term "wavenumber" (1) refers to the number of waveform cycles traveled by a photon in a fixed time. (2) refers to a quantity often expressed in cm-1. (3) refers to the product of frequency and Planck's constant. (4) refers to the distance corresponding to one cycle of a waveform. c. An instrument used to measure transmittance (1) must have a monochromator. (2) must have a detector for measuring light intensity. (3) must have the ability to ratio the light intensities measured with and without the sample. (4) all of the above. d. The Beer-Lambert Law (1) states that transmittance is linearly related to concentration. (2) requires that the product of absorptivity and pathlength be known before absorbance can be related to concentration. (3) requires that absorptivity be independent of wavelength. (4) cannot be used if more than one absorbing species is present in a sample. e. A D2 arc lamp (1) provides a continuous output in the infrared spectral region. (2) is based on the flow of current through a tungsten filament. (3) uses iodine to prevent the darkening of the lamp envelope. (4) is based on ultraviolet light emission from excited D2 species.
Chemistry 325
Instrumental Analysis
February 4, 2004
f. A least-squares analysis using the model y^ = mx + b (1) is based on the calculation of m and b such that the sum of squared errors is a maximum. (2) seeks values of m and b that will produce the smallest value of the standard error of estimate. (3) cannot be used with absorbance vs. concentration data due to limitations in the Beer-Lambert Law. (4) none of the above. g. A photon with a frequency of 6×1014 cycles/sec is (1) an ultraviolet photon. (2) a visible photon. (3) an infrared photon. (4) none of the above. h. For an analysis in which the measurement signal is in Volts and the analyte is determined in units of mg/L, the limit of detection (1) is expressed in units of Volts (2) is expressed in units of mg/L (3) is expressed in units of L/mg (4) is expressed in units of Volt-L/mg i. Which of the following statements is false regarding the absorption of photons by molecules? (1) absorption of a photon results in a change in the energy state of the molecule. (2) there is a correspondence between the energy of the photon and the difference in energy between the initial and final energy states (i.e., the states before and after the absorption) of the molecule. (3) the energy associated with electronic transitions is greater than the energy corresponding to a vibrational transition. (4) none of the above. j. Infrared photons (1) can only be absorbed by molecules with a bond dipole. (2) can only be absorbed when the photon frequency matches a vibrational frequency of the molecule. (3) can only be absorbed when their energy matches the difference in energy between two vibrational states. (4) all of the above.
Chemistry 325
Instrumental Analysis
February 4, 2004
k. A globar (1) is a rod of SiC that is resistively heated to produce infrared light through emission of blackbody radiation (2) is based on the production of an electrical arc within a rod of crystalline SiC. (3) is a type of ultraviolet light source commonly used in spectroscopy. (4) employs a halogen gas to prolong its lifetime. 2. (40 points) Answer five of the following: a. Name three regions of the electromagnetic spectrum. Visible Infrared Ultraviolet, etc.
b. A photon has an energy of 5.68×10-19 Joules. What is its wavelength in nm?
350 nm
c. Differentiate between single-beam and double-beam spectrometers.
Single-beam: one beam path through either reference or sample cell. Must alternate between reference and sample measurements. Cannot adjust for changes in source intensity and detector sensitivity in real time. Double-beam: two beam paths allow sample and reference cells to be mounted simultaneously. Optical chopper alternates beam between reference and sample cells. Allows real-time adjustment for changes in source intensity and detector sensitivity. Compatible with wavelength scanning.
Chemistry 325
Instrumental Analysis
February 4, 2004
d. Differentiate between the terms “sensitivity” and “selectivity”. Sensitivity: change in signal relative to change in concentration (corresponds to slope of calibration model). Selectivity: resistance of measurement to interference from sample matrix. Selectivity with respect to a given interference is defined quantitatively as the ratio of the sensitivity to the analyte to the sensitivity to the interference.
e. A 1.0x10-4 M solution is placed in a 1.00 cm pathlength cell and the absorbance is measured as 0.113 at 400 nm and 0.166 at 450 nm. Given that the concentration and pathlength are identical, why does the absorbance change? Absorbance is the product of absorptivity, path length and concentration. Absorptivity is a property of the analyte and changes as a function of wavelength (i.e., the probability that the analyte absorbs varies with wavelength).
f. Describe the mechanism by which infrared photons are absorbed. Vibration of a bond dipole (partially charged bonding atoms) generates an electric field at the vibrational frequency. If this frequency matches the frequency (energy) of an incoming photon, energy transfer can occur and the amplitude of the vibration increases.
Chemistry 325
Instrumental Analysis
February 4, 2004
3. (10 points) Compound X has an absorptivity of 703 g-1cm-1L. The transmittance of a solution of X is measured in a 1.00 cm pathlength cell and found to be 20.6%. Compute the concentration of the solution of compound X in g/L.
A = -log(T) = -log(.206) = 0.686 C = 0.686/(703)(1) = 0.000976 g/L
Chemistry 325
Instrumental Analysis
February 4, 2004
4. (10 points) A determination of Mg (AW=24.3) concentration (C, mg/L) in water based on an absorbance (A) measurement produced the following calibration model: A = 0.0191C + 0.0113 A 0.1145 g mineral sample was digested and diluted to 100.00 mL. A 7.00 mL aliquot of this sample was diluted to 100.00 mL and the absorbance of this solution was determined to be 0.203. Compute the weight percent of Mg in the original steel sample.
0.203 = 0.0191C + 0.113 --> C = 10.0 mg/L (10.0 mg/L)(0.1 L) = 1.00 mg total in analyzed solution (1.00 mg / 0.007 L) (0.1 L) = 14.3 mg total in original solution (14.3 mg / 114.5 mg)(100) = 12.5%
