IB Chemistry HL: Topic 11.1 (Uncertainties)

Question

If x = 749 ± 5 and y = 34.8 ± 0.7, which one of the following will have the greatest percentage uncertainty?

A. x + y

B. x - y

C. x/y

D. x√y

Trying to convince my teacher that it is A, otherwise I will get marked down to a very low grade.

Answer 1

Since this was asked almost 2 months ago, you probably don't need this answer anymore, but in case you do.

The uncertainties will be as follows (assuming simple uncertainty calculations, not standard deviations):

A. (749 ± 5) + (34.8 ± 0.7) = (749 + 34.8) ± (5 + 0.7) = 783.8 ± 5.7 = 784 ± 6

B. (749 ± 5) - (34.8 ± 0.7) = (749 - 34.8) ± (5 + 0.7) = 714.2 ± 5.7 = 714 ± 6

C. (749 ± 5) / (34.8 ± 0.7) = (749 / 34.8) ± (749 / 34.8) × [(5 / 749) + (0.7 / 34.8)] = 21.52 ± (749 / 34.8) × (0.0268) = 21.52 ± 0.58 = 21.5 ± 0.6

D. (749 ± 5) × (34.8 ± 0.7)^0.5 = (749 × 34.8^0.5) ± (749 × 34.8^0.5) × [(5 / 749) + 0.5 × (0.7 / 34.8)] = 4418.47 ± (749 × 34.8^0.5) × (0.0167) = 4418.47 ± 74 = 4420 ± 70

For percent uncertainty:

A. (6 / 784) × 100% = 0.77%

B. (6 / 714) × 100% = 0.84%

C. (0.6 / 21.5) × 100% = 2.8% ← highest percent uncertainty, sorry!

D. (70 / 4420) × 100% = 1.6%