Sample Laboratory Report I
Includes propagation of error treatment
Purpose: To determine the amount of citric acid in a mixture of unknown citric acid concentration.
Procedure: A solution of sodium hydroxide was standardized by titration against a known mass of oxalic acid dihydrate. The unknown was then titrated with the standard base to determine the amount of acid present.
Data:
Standardization of base
|
mass of oxalic acid dihydrate, g |
volume of sodium hydroxide, L |
|
0.1300 |
0.01672 |
|
0.1206 |
0.01549 |
|
0.1254 |
0.01612 |
|
0.1225 |
0.01556 |
|
0.1251 |
0.01577 |
Unknown
|
mass citric acid, g |
volume base, mL |
|
0.3829 |
21.15 |
|
0.4443 |
24.89 |
|
0.3925 |
21.99 |
|
0.3892 |
21.81 |
Calculations:
Sample calculation of concentration of sodium hydroxide
|
0.1300 g acid |
1 mol acid |
2 mol base |
= 0.1234 M NaOH |
|
0.01672 L base |
126.064 g acid |
1 mol acid |
Sample calculation of estimated error in the standardization of the base
Each volume delivered required two volume readings with an estimated error of 0.02 mL. Therefore for the estimated uncertainty in the volume is sqrt(0.022 +0.022) = 0.03 mL. The estimated error in the mass was 0.0001 g. The estimated error in the concentration is
c = 0.1234 * sqrt[ (0.03/16.72)2 + (0.0001/0.5201)2 + (0.001/126.064)2 ]
c = 0.0002
The calculated concentrations and the average and standard deviation are given below.
|
mass of oxalic acid dihydrate, g |
volume of sodium hydroxide, L |
concentration of sodium hydroxide, M |
|
0.1300 |
0.01672 |
0.1234 |
|
0.1206 |
0.01549 |
0.1235 |
|
0.1254 |
0.01612 |
0.1234 |
|
0.1225 |
0.01556 |
0.1249 |
|
0.1251 |
0.01577 |
0.1258 |
|
average, M |
0.1242 |
|
|
stdev, M |
0.0011 |
The value 0.1258 is suspect. The Q test (page 3-4 of the laboratory manual) was applied as follows:
Qexp = (0.1258-0.1249)/(0.1258-0.1234) = 0.38. Qcrit for five values is 0.64. Therefore all values are retained.
The median value is 0.1235 M and will be used for further calculations.
The standard deviation is six times the estimated uncertainty, therefore the experimental uncertainty will be used for further calculations.
Sample calculation of the per centage of citric acid in a mixture of unknown concentration.
|
0.02115 L base |
0.1235 mol base |
1 mole acid |
192.12 g acid |
100 |
=43.69% citric acid |
|
0.3829 g unknown |
L base |
3 mole base |
Mol acid |
The estimated uncertainty on the per centage citric acid is
p = 43.69 * sqrt[ (0.03/21.15)2 + (0.0011/0.1242)2 + (0.01/192.12)2 + (0.0001/0.3829)2]
p = 0.4
The calculated per centage citric acid in the unknown, along with the average and standard deviation is given below.
|
mass citric acid, g |
volume base, mL |
% citric acid |
|
0.3829 |
21.15 |
43.69 |
|
0.4443 |
24.89 |
44.31 |
|
0.3925 |
21.99 |
44.31 |
|
0.3892 |
21.81 |
44.32 |
|
average |
44.2 |
|
|
stdev |
0.3 |
The value 43.69 is suspect. The Q test was applied as follows:
Qexp = (44.31-43.69)/(44.32-43.69) = 0.98. Qcrit for four values is 0.76. Therefore the suspect datum is rejected.
|
mass citric acid, g |
volume base, mL |
% citric acid |
|
0.4443 |
24.89 |
44.31 |
|
0.3925 |
21.99 |
44.31 |
|
0.3892 |
21.81 |
44.32 |
|
average |
44.31 |
|
|
stdev |
0.01 |
The new average and standard deviation is 44.31 +/- 0.01.
The standard deviation is low relative to the estimate based on propagation of error from the standardization and the higher estimate will be used.
Conclusion.
The unknown consists of 44.3 +/- 0.4 % citric acid.
Sample Laboratory Report II
Includes propagation of error treatment
Purpose: To determine the amount of citric acid in a mixture of unknown citric acid concentration.
Procedure: A solution of sodium hydroxide was standardized by titration against a known mass of oxalic acid dihydrate. The unknown was then titrated with the standard base to determine the amount of acid present.
Data:
Standardization of base
|
mass of oxalic acid dihydrate, g |
volume of sodium hydroxide, L |
|
0.1300 |
0.01672 |
|
0.1206 |
0.01549 |
|
0.1254 |
0.01612 |
|
0.1255 |
0.01611 |
|
0.1251 |
0.01577 |
Unknown
|
mass citric acid, g |
volume base, mL |
|
0.3829 |
21.15 |
|
0.4443 |
24.89 |
|
0.3925 |
21.99 |
|
0.3892 |
21.81 |
Calculations:
Sample calculation of concentration of sodium hydroxide
|
0.5201 g acid |
1 mol acid |
2 mol base |
= 0.1234 M NaOH |
|
0.1672 L base |
126.064 g acid |
1 mol acid |
Sample calculation of estimated error in the standardization of the base
Each volume delivered required two volume readings with an estimated error of 0.02 mL. Therefore for the estimated uncertainty in the volume is sqrt(0.022 +0.022) = 0.03 mL. The estimated error in the mass was 0.0001 g. The estimated error in the concentration is
c = 0.1234 * sqrt[ (0.03/16.72)2 + (0.0001/0.5201)2 + (0.001/126.064)2 ]
c = 0.0002
The calculated concentrations and the average and standard deviation are given below.
|
mass of oxalic acid dihydrate, g |
volume of sodium hydroxide, L |
concentration of sodium hydroxide, M |
|
0.1300 |
0.01672 |
0.1234 |
|
0.1206 |
0.01549 |
0.1235 |
|
0.1254 |
0.01612 |
0.1234 |
|
0.1255 |
0.01611 |
0.1236 |
|
0.1251 |
0.01577 |
0.1258 |
|
average, M |
0.1239 |
|
|
stdev, M |
0.0011 |
The value 0.1258 is suspect. The Q test (page 3-4 of the laboratory manual) was applied as follows:
Qexp = (0.1258-0.1236)/(0.1258-0.1234) = 0.92. Qcrit for five values is 0.64. Therefore the suspect datum is rejected.
|
mass of oxalic acid dihydrate, g |
volume of sodium hydroxide, L |
concentration of sodium hydroxide, M |
|
0.1300 |
0.01672 |
0.1234 |
|
0.1206 |
0.01549 |
0.1235 |
|
0.1254 |
0.01612 |
0.1234 |
|
0.1255 |
0.01611 |
0.1236 |
|
average, M |
0.1235 |
|
|
stdev, M |
0.0001 |
The standard deviation of the replicate data (0.0001) is less than the uncertainty estimated by propagation of the error for the techniques used (0.0002), therefore the experimental uncertainty will be used for further calculations. The concentration of the base is 0.1235 +/- 0.0002 M.
Sample calculation of the per centage of citric acid in a mixture of unknown concentration.
|
0.02115 L base |
0.1235 mol base |
1 mole acid |
192.12 g acid |
100 |
=43.69% citric acid |
|
0.3829 g unknown |
L base |
3 mole base |
Mol acid |
The estimated uncertainty on the per centage citric acid is
p = 43.69 * sqrt[ (0.03/21.15)2 + (0.0001/0.1235)2 + (0.01/192.12)2 + (0.0001/0.3829)2]
p = 0.07
The calculated per centage citric acid in the unknown, along with the average and standard deviation is given below.
|
mass citric acid, g |
volume base, mL |
% citric acid |
|
0.3829 |
21.15 |
43.69 |
|
0.4443 |
24.89 |
44.31 |
|
0.3925 |
21.99 |
44.31 |
|
0.3892 |
21.81 |
44.32 |
|
average |
44.2 |
|
|
stdev |
0.3 |
The value 43.69 is suspect. The Q test was applied as follows:
Qexp = (44.31-43.69)/(44.32-43.69) = 0.98. Qcrit for four values is 0.76. Therefore the suspect datum is rejected.
|
mass citric acid, g |
volume base, mL |
% citric acid |
|
0.4443 |
24.89 |
44.31 |
|
0.3925 |
21.99 |
44.31 |
|
0.3892 |
21.81 |
44.32 |
|
average |
44.31 |
|
|
stdev |
0.01 |
The new average and standard deviation is 44.31 +/- 0.01.
The standard deviation (0.01) is low relative to the estimate based on propagation of error from the standardization (0.07) and the higher estimate will be used.
Conclusion.
The unknown consists of 44.31 +/- 0.07 % citric acid.