Why do we do "Trial Runs"?

Many exercises involve analysis of a substance whose composition or concentration is not known in advance. Such substances can be a sample of a household substance, an unknown, etc. This makes it impossible to know for sure the amount of the substance to use so as to insure that:

• we use optimal amounts of any reagents that we will use in the analysis of the unknown substance, or
• we use an appropriate amount of the unkown substance to insure that a technique will work properly (e.g., spectrophotometry)

The solution is to analyze an arbitrary amount (weight, volume, concentration) of the unknown substance by the analytical procedure we wish to use. We hope to get a result which provides guidance to what amount (weight, volume, concentration) of the unknown will give us the desired range, precision and/or accuracy.

What determines the "desired range, precision and/or accuracy"

Most of the analytical techniques we employ in the laboratory course involve either volumetric or gravimetric techniques.

For a 50 mL buret (Class A), the intrinsic error of the device is +/- 0.05 mL. [ I.e., to be class A, the delivered volume must be within 0.05 mL (1 drop) of the nominal volume. This assumes that the initial and final levels in the buret are read to their full capability - the nearest 0.02 mL].

A volume of 0.05 mL represents 0.1 % error in the delivery of 50 mL, 0.2 % error for 25 mL, 0.5% error at 10 mL and a 5% error if 1 mL is discharged.

We choose to compromise by using 25 +/-  3 mL as a TARGET VOLUME whenever a buret is used for a titration. This will insure that the percent error introduced through use of the buret is not more than 0.2%

A typical analytical balance has an intrinsic error of +/- 0.3 mg. To insure a percent error in weight consistent with our buret (0.2%), we should normally weigh samples of no less than ~150 mg of a substance. This then is a TARGET WEIGHT for the general use of the analytical balance -- again insuring that the error introduced through weighing is not more than 0.2%.

The idea of a desired range can arise when we are dealing with an instrument such as a spectrophotometer. E.g., if absorbances can be read to appropriate precision in the range A = 0.10 - A = 2.00 ( corresponding to 1% < %T < 79%), we would need to limit the concentration range that we use to insure that the absorbance falls in that range. (This will, of course, depend on the absorptivity of the substance in question.).

Desired or prescribed ranges can also arise because of instrumental limitations.

To meet the above criteria, we perform a TRIAL RUN - applying the analytical technique to an arbitrary amount of the unknown substance.

What is the next step after the trial run?

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Case 1: Titrating a weighed sample

We perform a trial run using 0.2134 g of our "unknown", It requires 15.02 mL of a reagent in a titration using a buret. We are now in a position to calculate the amount that will be necessary to meet our desired range, precision and accuracy.

As noted above, our target volume for a buret is 25 +/- 3 mL. How much of the unknown would be required to consume 25 +/- 3 mL of our reagent?

0.2134 g requires 15.02 mL
X         g requires  25 +/- 3 mL

0.2134 / 15.02 = X / (25 +/- 3)

X = 0.2134 * (25 +/- 3) / 15.02 = 0.36 +/- 0.04 g

Weighing an amount between 0.32 g and 0.40 g will meet our desired buret precision and target volume.

What Next?

HOWEVER, it is a waste of time (and virtually impossible, if weighing by difference) to try to weigh out a prescribed amount. We can quickly weigh an amount approximately equal to the desired amount. Suppose we do, and the actual sample weighs 0.3572 g. That certainly meets or minumum weight criterion (> 150 mg) and since it is within the calculated range above, will insure that we are close to our target volume.

But, we can extract even more information. How much of our reagent can we expect this weight of unknown to require in the titration? Using the ACTUAL weight (0.3572 g) , we can calculate with some precision, where to expect the end point of our regular titration.

0.2134 g requires 15.02 mL
0.3572 g requires  Y mL

0.2134 / 15.02 = 0.3572 / Y

Y = 0.3572 * 15.02 / 0.2134 = 25.11 mL ~ 25 mL

certainly within our prescribed target of 25 +/- 3 mL

Adjusting amount of unknown based on amount of product

This is a case where a limit on the range of device is determined by a device. Suppose we perform a trial run in which we generate a gas from a given amount of a substance of unknown composition. Our gas collection device is a syringe with a maximum capacity of 100 mL. We would like to weigh an amount of our unknown that produces between 60 and 80 mL of gas.

Suppose our trial run using 0.2068 g of our "unknown" produces 35.0 mL of gas. How much of the unknown should we weigh?

0.2068 g produces 35.0 mL
X         g produces  70 +/- 10 mL

0.2068 / 35.0 = X / (70 +/- 10)

X = 0.2068 * (70 +/- 10) / 35.0 = 0.41 +/- 0.06 g

Weighing an amount between 0.35 g and 0.47 g will meet our desired gas volume.

What Next?

Again, we can quickly weigh an amount approximately equal to the desired amount. Suppose we do, and the actual sample weighs 0.4273 g.

How much of gas will this weight of unknown produce? Using the ACTUAL weight (0.4273 g) , we can calculate what volume of liberated gas to expect.

0.2068 g produces 35.0 mL
0.4273 g produces  Y mL

0.2068 / 35.0 = 0.4273 / Y

Y = 0.4273 * 35.0 / 0.2068 = 72.3 mL