The concentration of a sodium hydroxide solution is determined by titration against a standard solution of oxalic acid. The
absolute uncertainty in the calculated
concentration of sodium hydroxide can be
determined from the uncertainty in each of the measurements made during the determination.
Assuming that the uncertainty in the oxalic acid standard solution is insignificant, the uncertainties in the sodium hydroxide concentration depend on the volume delivered by the pipette (25.00
) and and the burette (50
), and the titre volumes (21.76
, 21.70
, 21.68
, 21.75
).
number of
measurements | k |
| 2 | 0.89 |
| 3 | 0.59 |
| 4 | 0.49 |
The
absolute uncertainty in in the volumes delivered depends on the manufacturer's specification for the piece of equipment used and has the unit of the measurement. these are given in the table below.
The
absolute uncertainty (standard deviation) in the average titre volume depends on the range of titres from which it is calculated and a correction factor known as
k. This depends on the number of measurements made.
This is calculated by multiplying the range of the titre set by
k (for above 0.08
× 0.49) = 0.0392
.
A simple method for finding the uncertainty in numbers that result from calculations:
If the calculation involves adding or subtracting, the absolute uncertainties in the data are added to give the absolute uncertainty in the answer.
If the calculation involves multiplying or dividing, the absolute uncertainities in the data must be first converted to percentage uncertainities which are then added to give the percentage uncertainty in the answer.
Example showing calculation of the absolute uncertainty in a calculated sodium hydroxide concentration (0.05203 )Convert each absolute uncertainty to a percentage uncertainty using uncertainty in the measurement specified by the manufacturer.
Add the percentage uncertainties because this number was calculated by multiplication and division of data.
Convert the total percentage uncertainty in the answer to an absolute uncertainty.
Multiply the decimal equivalent of the percentage uncertainty by the concentration.
Round the absolute uncertainty to one significant figure.
Round the calculated concentration so that the last digit is in the same decimal place as the absolute uncertainty.
| Quantity measured | Size of
measurement | Absolute uncertainty | % uncertainty |
| burette | 50.0 mL | burette
±0.2 mL | | 0.2 mL | × 100% = 0.40 % | | 50 mL | |
| pipette volume | 25.00 mL | pipette
±0.05 mL | | 0.05 mL | × 100% = 0.20 % | | 25 mL | |
average
titre
volume | 21.76 mL | standard deviation
0.039 mL | | 0.039 mL | × 100% = 0.18 % | | 21.76 mL | |
Total percentage
uncertainty in
concentration | (0.40 + 0.20 + 0.18)% = 0.78% |
Absolute uncertainty
in concentration | | 0.78 | × 0.05203 mol L–1 = 0.0004 mol L–1 | | 100 | |
Report oxalic acid
concentration as | 0.0520 ± 0.0004 mol L–1 |