Question

For my chemistry class we did a lab on "pKa determination of methyl red indicator", and for my lab report one of the questions asks to calculate the uncertainty (after calculating the average pka, etc.). Normally I would repeat the measurement 6 times to calculate the uncertainty, but due to limited starting materials I only did one complete measurement.

I am really confused on how to go about calculating the propagation of error for uncertainty for my calculations in this lab. (below are my results )

Table 3: Absorbance Values of the indicator solution in buffer solutions at different pH values.

Solutions	Volume of 0.01M CH3COONa (cm3)	Volume of 0.02M CH3COOH (cm3)	Indicator Stock (cm3)	Water (cm3)	pH	Absorba-nce at λHMR (at 470 nm)	Absorbance at λMR (at 421 nm)
1 (red)	25.0	50.0	10.0	To make up to the mark	4.67	1.961	1.230
2 (blue)	25.0	25.0	10.0	To make up to the mark	4.99	1.974	1.563
3 (green)	25.0	10.0	10.0	To make up to the mark	5.38	2.118	2.230
4 (orange)	25.0	5.00	10.0	To make up to the mark	5.68	1.982	2.166

A^u_{HMR, λMR} = 0.956

A^u_{HMR, λHMR}= 2.4654=2.47

A^u_{MR, λHMR} =1.8577= 1.86

A^u_{MR, λMR}= 2.3181= 2.32

Table 4: Computation of the pK_a values of methyl red indicator using Handerson-Hesselbalch equation.

S. No.	pH	[MR]	[HMR]	[MR-]/[HMR]	log[MR-]/[HMR]	pKa= pH-log[MR-]/[HMR]
1	4.67	0.293	1.60	0.513	-0.290	4.96
2	4.99	0.499	1.19	1.18	0.0703	4.92
3	5.38	0.882	4.53	4.53	0.656	4.72
4	5.68	0.875	6.04	6.04	0.781	4.90
Average value of pKa						4.88

Answer 1

SOLUTION:

Graphs should be at least one-third page in size with axes labeled and with units. Expand

the axes, if necessary, so that your curve fills the plot (i.e. no large rectangles of empty space in

the plot). Slopes and intercepts from curve fitting should always be given with uncertainties.

Include the uncertainty for the the pKa' values propagated from the curve fit values (see the Error

Analysis handout for instructions for representing uncertainties). (You do not need to propagate

the uncertainties of the volume measurements through to the final results. Just start with the

uncertainties in the fit coefficients).

Estimating the Expected Error in the Final Result Based on the Measurement Errors:

You can estimate an upper bound for the expected error in the result by using just one data point.

Least squares curve fitting will give a smaller error, since the result is based on multiple trials,

but doing the calculation with just one data point will give an upper bound for the final error. The

uncertainty in absorbance measurements is ±0.002 at best. Since using the Beer-Lambert Law for

calculating concentrations involves multiplication and division, the errors in the concentrations

from the absorbances propagate as relative errors (even though we used some matrix tricks in the

process). In other words, assume the relative errors in the concentrations result from the relative

errors in the number of absorbance measurements required to calculate the concentrations. The

uncertainty in pH measurements is ±0.03, unless extra care is taken.