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

 1.3 Chemical calculations

Errors or uncertainties Chemistry and all science depend on quantitative measurements in experiments. The results are expressed in three parts – a number, the units in which the number is given and an estimate of the error in the number. Basically there are two ways of estimating the error. If several measurements of a quantity can be made, the values are averaged to obtain a mean value and a standard deviation is calculated. In AS Chemistry the error is estimated from the uncertainties in the apparatus used, such as burette, pipette, balance and thermometer. The size of the uncertainty is determined by the precision of the apparatus. Uncertainties are usually written with a ± sign. The actual value of the measurement lies somewhere between your reading plus the uncertainty value and your reading minus the uncertainty value. The uncertainty (error) will be different for different pieces of apparatus. For any piece of apparatus, the uncertainty is taken as one-half of the smallest division on the apparatus, e.g. 0.1 ˚C on a 0.2 ˚C thermometer, 0.05 cm 3 on a burette (since the scale has marks of 0.1 cm 3 ) and 0.5 mg (0.0005 g) on a three-place balance (since it measures to 0.001 g). Remember: if you use two readings to work out a measurement, you’ll need to combine their uncertainties. Percentage error If you know the error in a reading that you’ve taken, you can use it to calculate the percentage error in your measurement. percentage error = error reading × 100 Worked examples 1. In a titration, the initial reading on a burette is 0.10 cm 3 and the final reading is 24.75 cm 3 . Calculate the percentage error in the titre value. The titre value is 24.75 – 0.10 = 24.65 cm 3 . The error on each burette reading is 0.05 cm 3 . Two readings have been used to find the titre value, so the total error is 0.05 + 0.05 = 0.10 cm 3 . percentage error = 0.10 24.65 × 100 = 0.406% 2. In an enthalpy of neutralisation reaction, the temperature of 100g of solution before the reaction was 18.6°C and after the reaction was 26.2°C. Calculate the percentage error caused by the thermometer and the error in the evaluation of the heat produced. (The thermometer was accurate to ±0.1°C and the specific heat capacity of the solution was 4.2Jg −1  °C −1 ) Temperature rise = 26.2 − 18.6 = 7.6°C % error = 0.20 7.6 = 2.63% Heat produced = 100 × 4.2 × 7.6 = 3192J Error in value of heat produced = ±2.63% of 3192J = ±83.9J

Practical check Mistakes and errors are different. An error is something that a skilled worker would find difficult to avoid, and is a consequence of the way the apparatus has been constructed and how readings can be made using it. A mistake is something that a skilled operator can avoid by being careful. Examples of avoidable mistakes in a titration are leaving the funnel in the burette or overshooting the end-point.

Knowledge check A student adds a known mass of magnesium to an acid. The balance used to weigh the magnesium can be read to three decimal places. These are his results: Mass of magnesium and container before adding to acid = 12.362 g Mass of container after adding magnesium to acid = 12.254 g Calculate the maximum percentage error in the weighing of the magnesium. 17

45 DRAFT