 
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, C_{x}, by the method of
standard addition. You measure the signal, S_{x}, from the unknown solution. Then
you add a small amount, V_{s}, of a standard solution having a concentration of C_{s}
and measure the signal again (V_{2}).
a) Show that if V_{s}.<<V_{x} then the concentration of unknown
is
where V_{T} = the total volume
Solution: Determine general equation for each
solution; apply approximation and simplify.
1.
General equations: 

2.
When V_{s}.<<V_{x}, then V_{x » }V_{T} 

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 fullwave 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 4bit 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 12bit 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  V_{1} and then to send it through a resistor on a summing
circuit for the  V_{1} and V_{2}. 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 signaltonoise 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, C_{6}H_{6
}if t = 42.7± 0.5 m s and V =
5.00± 0.08 V.
Solution: Substitute into above.
