General Chemistry Laboratory/Mathematics of Chemistry Laboratory
The following digits are always significant:
- all non-zero digits in the number
- all zeros between non-zero digits in the number
- all zeros right of the decimal point, and at the end of the number
- all zeros to the left of the written decimal point in numbers ≥ 10
For addition and subtraction, the final result should have the same number of decimal places as the added/subtracted value with the smallest number of decimal places.
For multiplication and division, the final result should have the same number of significant figures as the multiplied/divided value with the smallest number of significant figures.
In the Laboratory
Mass determined by reading a balance should be recorded to as many decimal places as read off the balance, with absolute error as determined by the precision of the balance. Mass differences calculated using a tare should use that number of decimal places in the recorded result.
For graduated cylinders, a general rule is to record the amount to one more decimal place than is marked. For 10mL graduated cylinders, record to the nearest 0.01mL. For 25mL to 100mL graduated cylinders, record to the nearest 0.1mL.
Use the precision determination given for the instruments used to determine the level of absolute error in recorded values.
For addition and subtraction, simply add absolute errors of each component in the calculation.
For multiplication and division, convert to relative error first. The relative error value of each component is determined by dividing the error value by the actual component value. The relative error values of all components are added, then multiplied by the final calculated result of the operations on the component values, to find the absolute error of the final result.
There are key calculations that are often used in the course of performing experiments in the chemistry laboratory.
- Isolated mass of substance = [mass of container and substance] - [mass of container]
- Percent yield = ([mass of product] / [mass of initial substance]) * 100