16. By accident you wind up mixing together 200.0 mL of a standardized solution of HCl (MW=36.50, concentration = 0.2040 M) with 300.0 mL of a standardized nitric acid solution (HNO3, MW=63.02, concentration = 0.1090 M)
a) Is the resulting mixture still suitable for use in titrating an unknown base sample? WHY or WHY NOT?
b) If you decide that the mixture is suitable for use what is the concentration value you would use for this resulting solution?

17. Given the following replicate measurements of volume: 350 mL, 348 mL, 354 mL, 350 mL, 351 mL, 347 mL ( y=2100, y2=735,030)
a) What is the uncertainty (absolute & relative) associated with the first measurement? ANS: 1 mL, 0.29%
b) What is the precision, expressed in % RSD for this set of measurements. SHOW HOW you arrive at your answer.
Note: Any calculations of a standard deviation are to be performed using the Sum-of-Squares Method.
c) Calculate the two estimates of central tendency that you know for this set of data. SHOW HOW you arrive at your answer.
d) Explain what the presence of systematic error does (if anything) to the results of b) and c).
e) Explain what the presence of random error does (if anything) to the results of b) and c)

f) Suppose a measurement value is given as 350.0 mL. SHOW HOW this is a better measurement than the measurement of 350 mL given above.

g) Suppose now that the 6 replicate measurements above refer to the volume of Pepsi measured from 6 cans drawn from the new soft-drink machines which recently materialized on campus. Examining the cans you note that they purport to contain 355 mL. Question: With 95% confidence, is the machine issuing drinks which contain the stated volume? SHOW HOW you arrive at your answer AND ALSO give the range of volumes you are 95% sure that the machine is issuing (And you're right; Coca-Cola would never have put you through all this).

18. You recently faced a situation where you were told to "add 250 mL of water" to solid AgNO3 to produce a solution needed for the chloride determination. You actually could have performed this 3 different ways, METHOD 1 — use the graduations of a beaker, METHOD 2 — use a graduated cylinder, or METHOD 3 — use a volumetric flask.

If you used a beaker, what you actually measured was 2.5 E2 mL. If you used a graduate (capable of holding enough volume) you actually measured 2.50 E2 mL. Finally if you used a suitable volumetric flask, you measured out 2.500 ×E2 mL.
a) Calculate the absolute and relative uncertainty in each case. Then SHOW which process results in the best (i.e. best-controlled) measurement ANS: 4%, 0.4%, 0.04%; volumetric flask best
b) When you actually did this, you may have used your 100-mL graduate. Explain clearly what effect this would have (you need not make calculations, but you should indicate what the results of the appropriate calculations would be), in comparison to using METHOD 2 above.

19. You and 5 of your colleagues invade McDonalds with the intention of actually checking out 6 of their "quarter-pounders". Your measurement (in lbs) are: .250, .246, .255, .248, .251, and .245.
(For these measurements y = 1.495 and y2 = .372571)
a) What is your best estimate of the actual weight of a "quarter pounder"?
b) If in fact the true weight of a "quarter pounder" is .250 lbs, what is the % relative error of your "experiment"?
c) What is the reproducibility, i.e., % Relative Standard Deviation of your experiment? ANS: 1.6% (range), 1.5% (SS) dd) Fresh from your success at McDonalds you take on a new challenge. The suspicion has arisen that there is too much grease coating the burgers served at another of Lexington's finest restaurants, Le Maison de Greasy Spoon & Cheap Inappropriate Wine. You gather together your same 5 colleagues and measure the grease thickness of 6 burgers with a set of calipers, obtaining the following set of measurements (in mm grease): 4.1, 3.3, 3.4, 4.4, 3.1, and 4.0 ( y = 22.3 and y2 = 84.23)

If the National Association of Greasy Spoons, INC has decreed that an acceptable coating of grease is 3.3 mm, can you, with 95% confidence, state that the burgers served at Le Maison, etc, etc contain more than the acceptable coating? SHOW all work and explain your reasoning carefully.

20. Calculate the pH of the following solutions:
a) A 0.0150 N solution of H2SO4 (assume both protons are lost). ANS: 1.82
b) A solution formed by mixing together 75.00 mL of 0.1005 M Benzoic acid (MW = 122.1, Ka = 6.3 × 10 5) and 45.00 mL of 0.1600 M KOH (MW = 56.10)

Clueless:

A standardization issue. Standardization says that you know the concentration of the solution to a high level of quality (4 sig figs for #mmoles of, in this case [H3O+], and also the volume).

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Hints:

Do the laws of sig figs allow you to determine the #mmoles of [H3O+] for each individual solution before they are inadvertently mixed? If so, you can determine to a high level of quality the #mmoles of [H3O+] in the final mixture of solutions. You may assume that the volumes will add accurately.

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Clueless:

This is a comprehensive trip through statistical manipulations, followed by a typical statistical decision-making problem. As such it is very similar to other stat problems in this set of problems.

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Hints:

Parts a) through f) are almost definition-type questions. Part g) is the decision-making issue. It is handled in the usual manner:

1. First point, always. Statistics works on notion that measurements are REPLICATES. If you see a "suspicious" looking value (high or low) it's always conceivable that it is not a replicate, but that a GROSS ERROR crept into that (and only that) measurement at the time it was taken, resulting in the anomalous value. Here the values look pretty close to each other, suggesting the non-likelihood of an outlier, but they (the highest and the lowest) can be always tested via a Q-test.
1. Determine what the Decision Limit is, the value to be tested against.
1. Determine what you think the value for the volume of Pepsi being delivered really is. Almost always the mean value is the preferred choice. Almost certainly it will be numerically different than the decision limit.
1. Now determine what the effect of random error (in 95% of the cases) will be on this mean value. Do this by the calculation of a 95% Confidence Interval. This will allow you to add and subtract the 95% C.I. to the mean getting you a range of values, centered by the mean. This range of values are your 95% Confidence Limits.
1. See where your Decision Limit lies, with respect to the 95% "Confidence Limit Box" you have built around your mean value. If the mean is "inside the box" you have not demonstrated a real difference between your mean and the D.L. If "outside the box" you declare (with only 95% assurance, however) that the soft drink machines are NOT delivering the volume specified by the Decision Limit.

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Clueless:

This is a quality of measurement issue. The significant figures given to you tell you the expected quality. Your job is to ascertain which piece of equipment, a beaker, a graduate, or a volumetric flask, will be adequate to achieved the quality implied in the way the desired volume, "250 mL" , has been given to you.

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Hints:

You are calculating the Relative Uncertainty in each case. In part b) the idea is that repeated use of a graduate would be expected to lower the overall quality achievable. You are not presently required to perform this particular manipulation.

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Clueless:

This is another trip through statistical manipulations, followed by a typical statistical decision-making problem. As such it is very similar to other stat problems in this set of problems.

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Hints:

Parts a) through c) are almost definition-type questions. Part d) is the decision-making issue. It is handled in the usual manner:

A. First point, always. Statistics works on notion that measurements are REPLICATES. If you see a "suspicious" looking value (high or low) it's always conceivable that it is not a replicate, but that a GROSS ERROR crept into that (and only that) measurement at the time it was taken, resulting in the anomalous value. Here there is no obvious candidate of an outlier, but they (the highest and the lowest) can be always tested via a Q-test.
B. Determine what the Decision Limit is, the value to be tested against.
C. Determine what you think the value for the thickness of grease on the burgers really is. Almost always the mean value is the preferred choice. Almost certainly it will be numerically different than the decision limit.
D. Now determine what the effect of random error (in 95% of the cases) will be on this mean value. Do this by the calculation of a 95% Confidence Interval. This will allow you to add and subtract the 95% C.I. to the mean getting you a range of values, centered by the mean. This range of values are your 95% Confidence Limits.
E. See where your Decision Limit lies, with respect to the 95% "Confidence Limit Box" you have built around your mean value. If the mean is "inside the box" you have not demonstrated a real difference between your mean and the D.L. If "outside the box" you declare (with only 95% assurance, however) that the burgers do NOT have the value specified by the Decision Limit.

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Clueless:

A straight calculation of pH in Part a). Part b) is a mixing problem.

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Hints:

Part a) Here you need to know the definition of pH. You also need to know whether H2SO4 is a strong acid, weak acid, or has NO acid/base properties. Finally, you'll need to be able to convert Normalities to Molarities if you decide to proceed with H2SO4.

Part b) The best way to proceed is to draw the pH line and place each formula on its respective position, complete with #mmoles, on the pH line. Then, using the "neighbors rule", decide whether a major reaction takes place. If so, readjust #mmoles and formulas until you have the composition of the solution after the major reaction. This should lead you to deciding how to proceed to calculate the pH of the final solution at equilibrium.

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