QUANTITATIVE ANALYTICAL CHEMISTRY

1 )Volumetric (titrimetric)

analysis

Acid-Base

preciptimet

ry

Complexmetry

Redox

2 )Gravimetric analysis

3 )instrumental analysis

Electrochemistry

Spectrophotometry

Spectrofluorometry

Flame photometric methods

Statistics الجليل: عبد محمد د

Redox theory . حريه. د أ

Redox application . عزقل. حسن د أ

Complexometry . سميحه. د أ

STATISTICS

Error: deviation from the absolute value . Absolute error (E) : the difference between

an observed or measured value (O) and the true value (T) , with regard to the sign and it is reported in the same units as the measurement.

E = O – T Mean error: the difference between the

average of several measurements and the true value (T).

Relative Error: absolute or mean error (E) expressed as a percentage (%) of the true value (T)

Example,1: If a 2.62 g sample of material analyzed

to be 2.52 g. The absolute error (E) = 2.52 – 2.62 = -0.10

g. Example,2: In the titration of 10 ml of 0.1 N NaOH

with laboratory prepared 0.1 N HCl, the true value is 9.9 ml, and we have:

10.1, 9.9, 9.8, 10.2, 10.1 observed values,

So, Mean = summation of observed values / their number

= (10.1 + 9.9 + 9.8 + 10.2 + 10.1) / 5 = 10.02 ml.

And mean error = 10.02 – 9.9 = 0.12 ml.

In example,1: Relative Error = (-0.10/2.62) x 100% = -

3.8 % In example,2: Relative Mean Error = ( 0.12/9.9) x 100% = 1.21%

Types of Errors: (A) Determinate or systemic

(constant) errors: can be determined, (can be

avoided)

(B) Indeterminate (random, accidental or chance) errors:

cannot be determined or corrected.

Accuracy:agreement of a measurement with the true value.

Determination of accuracy:Absolute method Accuracy is determined from the relative

error; In example,1: Relative Error = (-0.10/2.62) x

100% = -3.8 % And accuracy = 100.0 – 3.8 = 96.2 %. In example,2: Relative Mean Error =

( 0.12/9.9) x 100% = 1.21% And accuracy = 100.00 – 1.21 = 98.79 %.

Example 3: In practical exam of volumetric analysis,

three students get the following results:

Precision :The agreement between several measurements of the same substance.

Mean (X):It is the arithmetic average of all measured values.

The range (w): the"spread":It is the difference between the highest

measurement and the lowest one. The median: It is the measurement in

the middle of the arranged measurements where the numbers of higher and lower measurements are equal.

standard deviation (s):

Variance =The square of the standard deviation = S2

Relative standard deviation (RSD)

  Coefficient of variation (C.V.) :

Example: Analysis of a sample of iron ore gave

the following % values: 7.08, 7.21, 7.12, 7.09, 7.16, 7.14,

7.07, 7.14, 7.18, 7.11. Calculate the mean, standard deviation,

the variance and coefficient of variation;

Find also the median and the range for these data.

Variance (S2) = 0.002 (b) The arranged data are: 7.07, 7.08, 7.09, 7.11, 7.12, 7,14,

7,14, 7.16, 7.18, 7.21 The median is : (7.12 + 7.14) / 2 = 7.13 The range is : 7.21 – 7.07 = 0.14

045.00020.0110

0182.0 deviation Standard

Coefficient of variation (C.V.) = 0.045 x 100

7.13= 0.063

Rejection of a result (The Q test): The Q test is used to determine if an

“outlier” is due to a determinate error or due to indeterminate error.

If it is due to a determinate error, it should be rejected.

If it is not due to a determinate error, then it falls within the expected random error and should be retained.

The ratio Q is calculated by arranging the data in decreasing order of numbers.

The difference (a) between the suspect number (the outlier) and its nearest neighbour number is divided by:

the range (w), which is the difference between the highest number and the lowest number,

Q = aw

x x x x x

a

w

Figure 2: Illustration of the calculation of Q.

The ratio is compared with the tabulated values of Q (see the Table).

If Q measured is equal or greater than the tabulated value, the suspected observation can be rejected.

If it is smaller than the tabulated value, the suspected observation is retained

Example: The following set of chloride analysis on

separate aliquots of serum were reported; 103, 106, 107 and 114 meq/L. one value appears suspect.

Determine if it may be rejected or not.

Answer: The suspected result is 114 meq/L. It differs from the nearest neighbor by (a) : 114

– 107 = 7 meq/L. The range (w) is : 114 – 103 = 11 meq/L. Therefore, Q = a/w = 7/11 = 0.64

The tabulated Q value (4 observations, 95% confidence level) is: 0.829

Since the calculated Q value is less than the tabulated Q value,

the suspected no. (114 meq/L) retained.

Significant figures ‘digit’ = 0, 1, 2, ………..8,9 A significant figure = is a digit which denotes the

amount of quantity in the place in which it stands. The digit 0 is a significant figure except when it is

the first figure in a number. In 1.2680 g and 1.0062 g 5 the zero is significant, but in the quantity 0.0025 kg 2 the zero is not significant, because 0.0025 kg = 2.5

g.

1 g means that it is between 0.9 and 1.1 g 1.0 g means that it is between 0.99 and 1.01 g 1.00 g means that it is between 0.999 and 1.001g Take 10.0 ml of Zn2+ sample, add 10 ml of NH3-

buffer Weigh 1.000 g of powdered drug sample, add 2 g of

hexamine reagent ….. 1 kg of tomato xxxxxxx 1.000 kg of gold !!! volume which is known to be between 20.5 ml and

20.7 ml should be written as 20.6 ml; but not as 20.60.

20.60 ml indicates that the value lies between 20.59 ml and 20.61 ml.

Confidence level No. of Observations Q90 Q95 Q99 3 4 5 6 7 8 9 10 15 20 25 30

0.941 0.765 0.642 0.560 0.507 0.468 0.437 0.412 0.338 0.300 0.277 0.260

0.970 0.829 0.710 0.625 0.568 0.526 0.493 0.466 0.384 0.342 0.317 0.298

0.994 0.926 0.821 0.740 0.680 0.634 0.598 0.568 0.475 0.425 0.393 0.372

Rejection quotient, Q, at different confidence levels