Why Weigh by Difference?Why Weigh by Difference?

The amounts of solid samples weighed in this course are generally small. I.e., often 500 mg or less.

Analytical balances can weigh objects with a precision of about 0.2 mg. • For a 500 mg sample, this is 100 x 0.2 / 500 = 0.04 %

We generally strive for better than 1% in precision and accuracy in exercises• 1% of 500 mg = 5 mg

• The analytical balance is certainly capable of providing well beyond this level of precision and accuracy

What else could keep us from achieving an accuracy of 1%?• The loss of sampleloss of sample in the process of transferring it from one

container to the next.

The loss of a 10 mg* sample by any means would constitute a • 100 x 10 / 500 = 2% error.

* For comparison, a drop of water weighs about 50 mg.

• Each time an intermediate container is used, there is a risk of some of the solid adhering to the container.

• This includes a spatula, watch glass, and especially paper.

• We would like to avoid the use of an intermediate container.

One way to accomplish this is:

• Weigh the final containerfinal container and leave it on the balance pan• Transfer solid until the final combined weight of the

container and the solid is the required amount• Subtract the weight of the container from the final

weight to get the weight of the transferred solid

Problem: The final container (beaker, flask, etc.) almost always exceeds the capacityexceeds the capacity of an analytical balance

(~100g)! The top loading balancetop loading balance can accommodate such weight, but it provides a precision of only about 20

mg How can we avoid intermediate containers when using the analytical balance?

Weighing by Weighing by difference!difference!

Weighing by difference will generally work in this course because substances that need to be weighed with high precision are almost always distributed in sample vials which can safely be put on the balance.

While this method may require several transfers, it will always work and will never cause an excessively heavy object to be put

on the balance pan.

• Weigh the sample vialsample vial

• Transfer solid until the weight of the sample vial and the solid is less than the original weight by the required amount

• Subtract the weight of the container and final solid from the initial weight to get the weight of the transferred solid

Suppose we wish to transfer a sample of Suppose we wish to transfer a sample of 200 mg200 mg

from a vial to a beakerfrom a vial to a beaker• When we are asked to perform such a transfer, it is understood

that the actual weight of the sample can usually be within 20% of the prescribed weight. For 200 mg this means 200 200 40 mg 40 mg..

• The steps are as follows:1. Weigh the vial and its contents2. Transfer a sample estimated to weigh 200 mg or lessor less

directly to the beaker. (The ability to estimate such amounts will improve with experience.)

3. Reweigh the vial and its contents

If the difference between initial and final weights is between 160 and 240 mg

- we have - we have accomplished our accomplished our

goal.goal.

If the difference between initial and final weights is less than 160 mg

- we need to - we need to transfer a (small) transfer a (small) additional amount additional amount

to the beakerto the beaker

If the difference between initial and final weights is greater than 240 mg - we must consider - we must consider whether to discard whether to discard

the sample. This will the sample. This will depend on the rest depend on the rest of the procedure.of the procedure.

Weigh the Vial and its Weigh the Vial and its contentscontents

14.7936 g

Remove Vial from Balance and Tap out Sample into Container

Reweigh Vial

14.6402 g14.7936 - 14.6402 = 0.1534 g = 153.4 mg

Result

• In this case, the transferred sample weighs considerably less than the desired amount

• 153.4 mg is less than 160 mg, which was the lower limitlower limit of an acceptable sample size (Remember, we are trying to weigh 200 40 mg)

• We therefore repeat the process by transferring an additional amount of material from the vial into the beaker.

• NOTE: We now have a much better basis for the visual estimation of the weight of a sample

Remove Vial from Balance and Tap out Remove Vial from Balance and Tap out Additional SampleAdditional Sample

Reweigh Vial

14.5783 g14.7936 - 14.5783 = 0.2153 g = 215.3 mg

ResultResult

• In this case, the weight of the total transferred sample is within the limits of acceptable size

• 215.3 mg is between 160 mg and 240 mg - the acceptable sample size

We have succeeded in our original goal!

When several weighings of samples of similar sizes are required, the subsequent samples are

much more easily estimated by eye.