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Uncertainty

I need to determine the uncertainty of my sodium hydroxide solution.

I added exactly 20.168g of solid sodium hydroxide to 250cm³ of distilled water.

1. The uncertainty of the weighing scales was ±0.001g
2. The uncertainty of the volumetric flask was ±0.25cm³

My question is, how do I determine the overall uncertainty of the concentration of the NaOH solution in the format: ± cm³

Reply 1

Morbo

Independent fractional uncertainties add like perpendicular vectors to give a resultant.

So fractional uncertainties in this case are:
1. ±0.001/20.168 = 4.96*10^-5
2. ±0.25/250 = 1.00*10^-3

Resultant fractional error/uncertainty:
U² = (4.96*10^-5)² + (1.00*10^-3)²

U = ±1.0012*10^-3

So this shows us that most of the error comes from your flask measurement (unsurprisingly).

And as far as I know, concentration is not measured in cm³, so I don't know why it wants that. I'm no chemist, but concentrations are in molar, right? Moles per litre of solution?

Molar mass of sodium hydroxide is 39.99g/mol, so you have 0.55434mol in 1/4litre of water. (I'll take the final volume of solution to be that of 1litre of water, which isn't the proper way, I know, but again - I'm not a chemist!)

That gives you 2.21735 M concentration (to too many sig figs). The error on this is:
2.21735*1.0012*10^-3 = 2.22*10^-3

So the final measurement is:
(2.217 ± 0.002) Molar, or alternatively 2.217(2) Molar.

I think :smile: