Chemistry Measurements & Calculations

Accuracy Accuracy is the closeness of a measurement to an accepted value. An accepted value is a value that has already been derived by either measuring or calculating and has been accepted as being the true value.

Precision Precision is how close a group of measurements come to each other. For example if you make three measurements of the same thing and get 2.5g, 2.4g, and 2.2g you would say these are precise measurements. Precision can also reflect the exactness of a measurement. An instrument that measures to a tenth of a unit is more precise than one that measures to a whole unit. The measurement 3.4 mL is more precise than 3 mL.

Examples of precision and accuracy Measurements can be accurate but not precise, precise but not accurate, neither accurate nor precise, or both accurate and precise. For example when measuring the density of copper (accepted value 8.96 g/mL) if your results are 9.0, 8.88, and 8.99 g/mL you would say your results are both accurate and precise. But if they were 10.0, 9.98, and 10.01g/mL they would be precise but not accurate. If your results were 10.0, 8.0, and 9.3g/mL you would say they are not precise but the average,9.1g/mL, of the measurements are fairly accurate. And if your results were 7.5, 10.5, and 12.0 g/mL you would say the results are neither accurate with and average of 10.0 g/mL, nor precise.

Significant Figures Significant figures (sig figs) are used in order that our results from calculations of measurements are not more precise than the measurements.

What digits in a number are significant? All nonzero numbers are significant. All zeros between nonzero numbers are significant. Zeros at the end of a number are significant if there is a decimal in the number Zeros at the beginning of a number are never significant

Exact Values Exact values have unlimited sig. figs. Examples of exact values are: count value conversion factors Ignore count values and conversion factors when determining the number of sig. figs. In your calculated results.

Significant Figures when recording data Always estimate to one place beyond the precision of your measuring instrument. For example if the instrument measures to tenths then estimate to hundredths. Place a decimal after zeros that have been measured to that precision. If a measurement is exactly twenty millimeters and the measuring instrument measures to 10s of mL then the measurement should be recorded as 20. mL. This shows you have measured to that precision.

Calculations with Sig. Figs. When adding and subtracting with measurements round the results to the same place as the measurement that is the least precise. Or to the measurement that has the left most uncertain digit. Example 2.34 g +3.6 g 5.94g rounds to 5.9g

Sig. Figs. When multiplying and dividing The results of multiplying or dividing with measurements should be rounded to the same number of sig. figs. as are in the measurement that has the least number of sig. figs. Example 4.5g/ 1.36 mL = 3.309 g/mL rounds to 3.3g/mL.

Rounding exact fives If you are rounding off an exact five there is no other numbers after the five then use this rule: If the number you are rounding is even, leave it, if it is odd, round it up to an even number. We use this rule so that our results are not skewed higher but average out between the rounding up and leaving at an even number.

Specific Heat The energy required to raise the temperature of 1 gram of pure substance 1K. Formula for specific heat is: cp = q/m x T cp = specific heat q= energy in Joules m= mass in grams T = change in temperature in Kelvin or Celsius