Analytical Chemistry Notes PDF

INTRODUCTION In a measurement the operator mainly takes care of three components: the system, some property being measured, and the instrument 2.2.1 Error Error is mathematically defined as the difference between the observed value and the true value: E=O–T where E is the error (absolute error), O...

INTRODUCTION In a measurement the operator mainly takes care of three components: the system, some property being measured, and the instrument 2.2.1 Error Error is mathematically defined as the difference between the observed value and the true value: E=O–T where E is the error (absolute error), O is the observed value of a measurement, and T is the true value. It is with regard to sign, and it is reported in the same units as the measurements Table 2.1: Expression of Error in Measurements in Volume of a Flask However, the absolute error is of little practical significance for a quantitative analysis.It is the relative error, that is, the error relative to the true value (E/T) expressed insuitable units, is of the practical importance as a measure of inaccuracy (or as aninverse measure of accuracy). 2.2.2 Types of Errors i) Determinate Errors ii) Indeterminate Errors Accuracy 2.4.1 The term accuracy is defined as the nearness of a measurement to its true value It is expressed in terms of error. Error (defined in section 2.2) is.(or accepted value) an inverse measure of accuracy. Less the error greater is the accuracy The most common being either in terms of percent relative error or in terms of relative accuracy in percentage Example 2.1 A sample was analyzed for desired constituent having 2.62 g as the true value. The results of three measurements were 2.50 g, 2.54 g, and 2.52 g. Find the error of the mean (mean error), the percent relative error and the relative accuracy of the mean of the measurements Solution Precision 2.4.2 Precision is defined as the reproducibility of measurements. It tells an agreement between the numerical values of replicate measurements It follows that the closer the results of replicate determinations are to each other, the more precise is the analysis considered to be. Precision in a common way is expressed in terms of deviation. Less the deviation more precise the result is. Deviation or apparent error is defined as the difference between the measured value and the mean (average) of the series of measurements Distinction between Accuracy and Precision The accuracy should not be confused with the precision. Good agreement in parallel determinations signifies that the determinations have been made under closely similar conditions, it does not guarantee the accuracy of the results. A method may be precise but may not be accurate if a large systematic error is made. On the other hand it is nearly impossible to have accuracy without good precision. The difference of the terms accuracy and precision can be illustrated by considering the shooting of series of bullets on the targets by three riflemen (A, B, C), shown in Figure 2.1 Example 2.2 The burette readings of titrations carried out by three students A, B and C are given below. Compare the accuracy and precision of the three students, if the true reading is 22.22 ml You can understand from the observed values and calculated mean values of titrations of three students that the results of student A are reproducible and the mean value resembles the true value. Hence the results of student A are both precise and accurate.A look of the titration results of student B shows that his results are reproducible but the mean value is slightly on the higher side than the true value. May be he might be taking the end point (colour change) on the higher side. Therefore, the results of student B are precise but not accurate. The readings of students C are spread in a wide range with a poor reproducibility. Hence his results are neither precise nor accurate 3.2.1 Mean arithmetic average of all the observations in the set of data: Median ,For an odd number of total observations (n is odd) the median is obtained directly as middle value For a set of even numbered total observations (n is even), the median is the average of the middle pair of observations 3.2.3 Mode The observation which occurs most frequently (i.e. with maximum frequency) in a series of observations is known as mode. It is yet another quick measure of central value if the number of observations is not too small. For example, the mode of the set of data: 12,6, 12,7, 12.9, 12,7, 12.6, 12.8, 13.0, 12.5, 12.6, the value 12.6 is the mode since this is occurring with maximum frequency (four times). 3.2.4 Deviation The error of a measurement can not be stated if the true value of the quantity is not known. It is meaningful then to take the difference between a particular measured value (observation) and the arithmetical mean of a series of measurements and this difference is called as its deviation for apparent error.A deviation is generally taken without regard to sign. It is defined mathematically as where, d is the deviation of the observation x of a finite sample from its mean x ,D is the deviation of an individual measurement from the population mean µ, and | | denotes that the difference is taken as absolute. The reproducibility of measurements is expressed in terms of various types of deviations 3.2.5 Average Deviation The average deviation (a.d.) or the mean deviation is the average of individual deviations where the symbols have their usual meanings The ratio of the average deviation to the mean is known as Relative Average Deviation (RAD) which can be expressed as percent average deviation when multiplied by 100 3.2.7 Range The difference between the largest and smallest values in a set of measurements is known as the range. It tells the spread of data. The range is often used, with appropriate factors that depend on the number of measurements, as a quick statistics to a rough estimate of precision. SAQ 1 Calculate the median for the data: 14.1, 13.8, 14.3, 13.6, 13.4 & 13.5 Example 3.1 In an iron determination (taking 1 g sample every time) the following four replicate results were obtained: 29.8, 30.2, 28.6 and 29.7 mg iron. Calculate the standard deviation of the given data  Significant Figures Scientific measurements are reported so that every digit is certain except the last, which is estimated. All digits of a measured quantity, including the certain one, are called significant figures. Counting Significant Figures Examples 1.54 (3 sig. figs.) 1. All non-zero digits are always significant. 45 (2 sig. figs.) 0.02503 (4 sig. figs.) 2. Interior zeros (zeros between nonzero numbers) are significant. 402 (3 sig. figs.) 3.00674 (6 sig. figs.) 3. Leading zeros (zeros at the beginning of a number) are NOT 0.103 (3 sig. figs.) significant. 0.000002 (1 sig. fig.) 4. Trailing zeros (zeros at the end of the number): 1.050 (4 sig. figs.) 1.00 x 103 (3 sig. figs.)  are significant if and only if there is a decimal point present 10 (2 sig. figs.) in the number OR they carry overbars. 1000 (1 sig. fig.)  are NOT significant otherwise. 190 (2 sig. figs.) 5. Exact numbers have an unlimited number of significant figures. 10 dm = 1m (unlimited sig. figs.) Significant Figures in Calculation Multiplication and Division Addition and Subtraction When multiplying or dividing measurements When adding or subtracting measurements with significant figures, the result has the same with significant figures, the result has the same number of significant figures as the number of decimal places as the measurement with the lowest number of measurement with the lowest number of significant figures. decimal places. 5.02 × 89.665 × 0.10 (3 sig. figs.) (5 sig. figs.) (2 sig. figs.) 2. 0 3 4 5 (4 d.p.) = 45.0118 0.07 (2 d.p.) 5.9 (1 d.p.) = 45 (round off to 2 sig. figs.) + 2. 9 9 7 5 (4 d.p.) - 2. 2 2 1 (3 d.p.) 5.892 ÷ 6.10 5.4125 5.6 79 (4 sig. figs.) (3 sig. figs.) = 5.41 (2 d.p.) = 5.7 (1 d.p.) = 0.96590 (3 sig. figs.) (1 sig. figs.) = 0.966 (round off to 3 sig. figs.) Practice Problems 1. How many significant figures are in each of the following? a) 3.405 b) 0.00289 c) 1030 d) 7.0040 x 10-3 e) 102.00 f) 0.000980 g) 9.80 2. Perform the following calculations to the correct number of significant figures a) 12.0550 + 9.05 b) 257.2 – 19.789 c) (6.21 x 103) (0.150) d) 0.0577 ÷ 0.753 e) 27.5 x 1.82 ÷ 100.04 f) (2.290 x 106) ÷ (6.7 x 104) g) [(28.7 x 105) ÷ 48.533] + 144.99 3. Round each of the following numbers to three significant figures: a) 342.79513 b) 9,845.8749 c) 0.000045389 d) 2.45555567 e) 76.89 f) 56.9971 References: Tro, Chemistry: A Molecular Approach 2nd ed., Pearson Brown/LeMay/Bursten, Chemistry: The Central Science, 12th ed., Pearson 3. a) 343; b) 9850; c) 0.0000454; d) 2.46; e) 76.9; f) 57.0 2. a) 21.11; b) 237.4; c) 652; d) 7.66 x 10-2; e) 0.500; f) 34; g) 5.93 X 104 1. a) 4; b) 3; c) 3; d) 5; e) 5; f) 3; g) 3 Answers