Chapter 2 Chemistry as a Quantitative

Science and a Science of Matter

1. Measurement 

Quantitative science pertains to measurable and systematic methodologies in scientific inquiry.

It focuses on numerical data to understand chemical reactions and properties.

Measurements such as molarity, pH, and concentration are central to quantitative chemistry.

Quantitative analyses help in determining the precise quantities of reactants and products.

Statistical methods in chemistry allow for accurate predictions and experimental designs.

2. Significant Figures

Significant figures (or significant digits) are the number of digits in a given value or a measurement, necessary to decide the accuracy and precision of measurement.

They are important in scientific or technical measurements.

“Significant” means important. They refer to the reliable digits in the given number, which are sufficient to convey accurate information. They also help us round off measurement values or the outcome of a calculation. 

Rule 1 - Non-zero digits are ALWAYS significant

Rule 2 - any zero contained between two non-zero numbers is significant

Rule 3 - leading zeroes are never significant

Rule 4 - final or trailing zeroes are significant only after a decimal point

eg.

1.005 - four significant figures (1, 0, 0, 5); the zeroes are automatically counted as they fall between two non-zero digits.

0.00500 - three significant figures (5, 0, 0); the leading zeroes do not count (as per Rule 3) but the two trailing zeroes are considered to be significant as they come after a decimal point. So in this example the three significant figures are the 5 and the final two zeroes.

0.005 - one significant figure (5); the leading zeroes do not fall between two non-zero digits and only the 5 is considered significant.

500.00 - five significant figures (5, 0, 0, 0, 0). The four trailing zeroes are all significant due to the decimal point which adds precision to the number.

3. Arithmetic using significant figures

Add up the number of significant figures to the right of the decimal part of each number used in the calculation.

Perform the calculation (addition or subtraction) as usual.

The answer must not contain more significant figures to the right of the decimal point than the fewest of any of the figures worked out in part 1. So for example if you are adding together two numbers with three and four significant figures to the right of the decimal point, the answer cannot have more than three significant figures to the right of the point.

eg. 1.18 + 2.2 = 3.38

As the answer cannot have more than 1 significant figure in the decimal part, you must round the result as appropriate, giving a final answer of 3.4.

3.3 - 1.55 = 1.75

Round the number to give a final answer of 1.8

Multiplication rules and division rules for significant figure calculations

Unlike the addition and subtraction example, you now must calculate the number of significant figures in each number in its entirely before performing the calculation, not just the decimal part. Once you have performed the calculation, the answer now must contain the same number of significant figures as the smallest total of them in the initial numbers.

eg. 3.1 x 3.5 = 10.85

However 10.85 has four significant figures and therefore must be rounded to 11, which has two. So in this case the correct answer is 11.

3.100 x 3.500 = 10.85

This answer (10.85) has four significant figures and therefore remains the correct one to use.