Chemistry 422 Exam I Name:

September 25, 1998

KEY

Instructions: Read the whole exam before starting to work on individual problems; work those that you find the easiest first. Budget you time!

1 We want to determine the concentration of an unknown, Cx, by the method of standard addition. You measure the signal, Sx, from the unknown solution. Then you add a small amount, Vs, of a standard solution having a concentration of Cs and measure the signal again (V2).

a) Show that if Vs.<<Vx then the concentration of unknown is

where VT = the total volume

Solution: Determine general equation for each solution; apply approximation and simplify.

1. General equations:
2. When Vs.<<Vx, then Vx VT
3. Simplify

b) The signal intensity was 38.44 for a solution of unknown concentration. When 0.05000 mL of a solution having a concentration of 0.2000 M was added to 25.00 mL of the unknown, the signal increased to 48.15. What was the concentration of the unknown solution?

Solution: Substitute into given equation and solve.

2 DC conversion:

a) Draw a circuit diagram of a full-wave rectifier and explain the principles of its operation;

Solution: See notes

b) A total voltage of 5.11 V was measured across two parallel resistors that had resistances of 15.00 W and 32.15 W . What is the current going through each resistor?

Solution: The voltage across each resistor is the same; simply use Ohm’s law twice. Ans.: 0.159 A and 0.341 A

3 Digital output using D/A converters:

a) The input voltage on a 4-bit D/A converter was 5.33 V what would the output voltage be for a digital output of 1011?

Solution:

b) What would be the relative error in the output of the D/A signal for a 12-bit D/A converter? Assume all of the error is equal to the smallest output voltage.

Solution:

4 Operational amplifiers:

a) Draw an operational amplifier circuit which allows you to perform the calculation:

. Be sure to include specific values for you resistors.

Solution: One possible configuration would be to use an inverting unity gain operational amplifier to make the output of that amplifier - V1 and then to send it through a resistor on a summing circuit for the - V1 and V2. The gain should be 6 and 8 respectively.

b) What are the properties of ideal operational amplifiers? Draw the equivalent circuit for one.

Solution: See notes and book.

5 Noise:

The following data were obtained for a voltage measurement on a noisy system: 1.37, 1.84, 1.35, 1.47, 1.10, 1.73, 1.54, 1.08

a) Assuming only random noise, what is the signal-to-noise ratio?

Solution: The signal to noise ratio will equal the mean divided by the standard deviation. This gives a S/N of 5.29 for this set of data.

b) How many measurements would have to be averaged to increase the S/N to 10?

Solution: The signal to noise ratio increases with the square root of the number of measurements. One could write:

6 Error:

In a time of flight mass spectrometer, the mass is determined by the flight time according to the equation:

a) Derive an equation that will allow you to calculate the relative error in the determination of the mass. Assume that e (the charge on an electron) and L (the length of the flight tube) are constants.

Solution: use the normal error equation, recognizing that m(V,t); take the derivative of the equation with respect to each variable and then simplify.

b) Determine the relative error in the calculation of mass of benzene, C6H6 if t = 42.7 0.5 m s and V = 5.00 0.08 V.

Solution: Substitute into above.