Chemistry 5640 Instrumental Analysis
Take-Home Examination
March 4, 2005
Due Friday, March 11, 2005 at 11:30 AM

Instructions: Answer the following 5 equal-valued questions on your own. Answers may be turned in either neatly hand written or typed (printed). Be sure to put your name on your response. Most everything required for successful performance is in the book or on the handouts received in class. You may not share your results with other students prior to the examination being graded and returned. You may ask me questions, either in person, or by e-mail (Stephen.Bialkowski@usu.edu). If I respond with important information, this information may be shared with the class, by me only, either verbally or by posting on the Chemistry 5640 internet home page (http://www.chem.usu.edu/~sbialkow/Classes/5640/Chem5640.html).

1) Thevenin’s equivalent circuits and measurement error
The electronic circuit for a common combination pH electrode may be accurately represented by a Thevenin equivalent circuit for a voltage (potential) source.

  1. The internal resistance of a pH electrode is very high, typically RS=20 MΩ (see section 23C-3 in the text), because the glass membrane is not very conductive. The potential for this source is, of course, variable; dependant on the solution pH, ionic strength, temperature, and presence of interfering species. Draw the Thevenin’s equivalent circuit for the electrode.
  2. Assuming that a measurement device can be represented as a single "load" resistance, RL, draw the circuit that results when the measurement device is being used to measure the potential.
  3.  Measurement devices have different load or input resistances. Calculate the relative % errors produced using the following measurement devices;
    1) An oscilloscope with an input resistance of 10 MΩ
    2) A low-quality voltmeter with an input resistance of 1 MΩ
    3) A voltage follower operational amplifier circuit with input resistance of 100 MΩ
  4. Which measurement device would you prefer to use? Why?
  5. Accurate chemical measurements are obtained only when one calibrates the apparatus, i.e., electrode and measurement device, with standard solutions of known pH. Can this procedure be used to overcome the electronic measurement errors associated with pH determinations using real measurement devices? If so, how would you perform the experiment?

2) Complex impedance and passive filters

  1. Using the imaginary capacitor reactance, show that the gain formulas (gain=Eout/Ein) for the high- and low-pass frequency filters using resistors and capacitors on the handout are correct.
  2. A band-pass filter can be constructed using series high- and low-pass filters. Draw the schematic diagram this band-pass filter.
  3. Predict how this circuit will function for a real filtering problem. Assume that the signal of interest is at 20 kHz. (i.e., voltages at other frequencies are noise.) Specify a set a two resistor and two capacitor values that would pass the 20 kHz signal. What is the gain formula of your circuit?
  4. Illustrate the frequency response of your filter by plotting logarithm of gain as a function of the logarithm of the angular frequency (w=2πf) from f=1 to f=1 MHz. Does your filter work as well as expected?

3) A zener regulated power supply.
In this problem you will describe the function of a “regulated” power supply. The power supply is to operate from the usual "household" wall plug (117 Volt, 60 Hz, AC) and is to supply DC voltage to a circuit.

  1. What is the output potential of this power supply?

  2. Explain the function of each component.

  3. What is the RC time constant? Is this sufficient to filter the bridge rectifier output?

  4. How much current passes through the resistor, assuming that the DC potential at the capacitor is 6.3 V, with no load resistor attached?

  5. When the power supply is attached to a load, the potential may drop below that regulated by the Zener diode. At what load resistance does this occur?

4) Operational amplifiers

  1. Design an analog computer to perform the function specified by the following equation.

  1. What would happen to the output potential if E1(t) were positive valued and the integration time were not periodically reset?
  2. Estimate the frequency response of the differentiator circuit illustrated in Figure 3-13 (d) of the text using the reactance of a capacitor (XC=1/2pfC). Is the differentiator a high- or low-pass circuit?
  3. Give some uses for the voltage follower circuit illustrated in Figure 3-7 of the text. What electronic characteristics of this circuit make it useful in measurement science?

5) Signals and Noise

  1. List the three main types of noise, give the formula, and give a physical explanation for each noise type.
  2. How is interference different from the fundamental noise described above?
  3. Assuming that only thermal and shot noise source terms are important, use the Thevenin’s equivalent circuit for the electrode in Question 1, measured with a 1 MW instrument, to estimate the noise voltage. For a pH electrode that follows the Nernst equation, how many pH units does this noise represent?
  4. What type of filter would be used to reject noise from a DC signal?