WJEC Chemistry for AS Level Student Book: 2nd Edition (Draft)

WJEC Chemistry for AS Level

In a volumetric titration we may have percentage errors from the burette, pipette and balance contributing to the total error. Usually at AS it is simpler and satisfactory to identify the largest error and use that on its own. For example, it is very rare for the percentage error in the balance to be significant. The result of a calculation using several pieces of data cannot have more significant figures than the least number given in any of the terms in the calculation. For example, solutions A and B react in a 1 : 1 mole ratio and 10.00cm 3 of solution B required 25.16cm 3 of solution A, the concentration of which was 0.10mol dm −3 . The concentration of B is thus 25.16 × 0.10 10.00  = 0.2516mol dm −3 . However, since the concentration of A is only known to 2 significant figures, that of B may only be written as 0.25mol dm −3 . Significant figures and decimal places In calculating the percentage error for the burette in the worked example the calculator gives 0.405679513. What does this mean? The last five numbers mean nothing; since the error is about 0.4%, that is 4 in a thousand, anything after the third or fourth significant figure has no physical significance. Since the fourth significant figure is 5 or above, the third figure may be rounded up to 0.406. It is important that full calculator outputs are not recorded as FINAL answers, only numbers having physical significance should be used. However, the full output may be used at intermediate stages in a calculation. A serious error is to destroy information gained in the experiment by over-shortening the result as when a concentration of 0.0946mol dm −3 is returned as 0.09 or even 0.1! These are the rules for working out significant figures: Zeros to left of first non-zero digit are not significant, e.g. 0.0003 has one sig. fig. Zeros between digits are significant, e.g. 3007 has four sig. figs Zeros to the right of a decimal point with a number in front are significant, e.g. 3.0050 has five sig. figs. Decimal places are the number of digits to the right of the decimal point so that 0.044 has 3 decimal places but only two significant figures. Stating the value to two decimal places would give a different value (0.04) than the correct significant figures (0.044). Always use significant figures and not decimal places when considering errors. Standard form and ordinary form Both forms are commonly used, the standard form being useful when large and small numbers are encountered. It is important that the same number of significant figures is used in both, e.g. ordinary form 0.0052mol dm −3 , standard form 5.2 × 10 −3  mol dm −3 , both have two significant figures.

Stretch & challenge

In a titration, for example, we might assume that the burette error is 0.4%, the pipette error is 0.2% and the weighing error 0.1%. We square these numbers, add them together and take the square root that gives a combined error of 0.46%, an estimate that is very little different from the 0.4% for the burette alone. So the weighing error can definitely be ignored.

Study point If an error is about three times larger than any other errors there is no need to consider the others at AS level.

18 Knowledge check State the number of significant figures for the following numbers; (a) 17.68 (b) 3.076 (c) 0.004 (d) 6.05 × 10 18  (e) 3000.0

46 DRAFT