Measurement in Chemistry: Uncertainties, SI Units, and Significant Figures

Measurement in Chemistry

Uncertainties in Measurements

Measurement is fundamental to all scientific disciplines, including chemistry. Every measurement contains some degree of uncertainty, which must be understood and reported appropriately. Data collected in experiments can be classified as either qualitative or quantitative.

• Qualitative Data: Non-numerical observations describing qualities or characteristics. Examples include color, texture, or the presence of a flame or smoke during a reaction.

• Quantitative Data: Numerical measurements, such as mass, volume, or temperature. These data are essential for calculations and analysis in chemistry.

• Example: In an experiment to determine the empirical formula of magnesium oxide:

  • Qualitative: "The magnesium burned with a bright, white flame."

  • Quantitative: "The mass of magnesium used was 1.24 g."

SI Units

Base SI Units

The International System of Units (SI) provides standard units for scientific measurements. Each physical quantity has a corresponding SI base unit.

Quantity	SI base unit	Symbol
Length	meter	m
Mass	kilogram	kg
Time	second	s
Temperature	kelvin	K
Amount of substance	mole	mol
Electric current	ampere	A
Luminous intensity	candela	cd

SI Prefixes

SI prefixes are used to express multiples or fractions of units, making it easier to handle very large or very small numbers.

Prefix	Symbol	Factor	Scientific Notation
nano	n	0.000 000 001	$10^{-9}$
micro	μ	0.000 001	$10^{-6}$
milli	m	0.001	$10^{-3}$
centi	c	0.01	$10^{-2}$
deci	d	0.1	$10^{-1}$
deca	da	10	$10^{1}$
hecto	h	100	$10^{2}$
kilo	k	1,000	$10^{3}$
mega	M	1,000,000	$10^{6}$
giga	G	1,000,000,000	$10^{9}$

Derived SI Units

Derived units are combinations of base units used to express other physical quantities.

Quantity	Derived SI unit	Symbol	Expressed in base units
Area	square meter	m2	m2
Volume	cubic meter	m3	m3
Velocity	meter per second	m s-1	m s-1
Density	kilogram per cubic meter	kg m-3	kg m-3
Force	newton	N	kg m s-2
Pressure	pascal	Pa	kg m-1 s-2
Energy	joule	J	kg m2 s-2

Measurement Devices

Precision and Accuracy in Measurement

Different devices provide different levels of precision. For example, rulers with more divisions allow for more precise length measurements, and balances with more decimal places provide more precise mass measurements.

• Precision: The degree to which repeated measurements under unchanged conditions show the same results.

• Accuracy: How close a measured value is to the true value.

• Example: A balance that reads to 0.001 g is more precise than one that reads to 0.1 g.

Significant Figures

Definition and Importance

Significant figures (sig figs) are the digits in a measurement that are known with certainty plus one digit that is estimated. They reflect the precision of a measurement and are crucial for reporting scientific data accurately.

• All nonzero digits are significant. (e.g., 123 has 3 significant figures)

• Captive zeros (zeros between nonzero digits) are significant. (e.g., 105 has 3 significant figures)

• Trailing zeros in numbers with a decimal point are significant. (e.g., 1.00 has 3 significant figures; 100. has 3 significant figures)

• Trailing zeros in numbers without a decimal point are not significant. (e.g., 200 has 1 significant figure)

• Leading zeros (zeros before nonzero digits) are never significant. (e.g., 0.012 has 2 significant figures)

• Exact numbers (such as counted objects or defined quantities) have an infinite number of significant figures.

Examples

• 0.2 (1 significant figure) vs. 0.20 (2 significant figures)

• 2300 (2 significant figures)

• 1.00 (3 significant figures)

• 0.003000 (4 significant figures)

Rounding Rules

• If the digit to be dropped is greater than or equal to 5, increase the preceding digit by 1.

• If the digit to be dropped is less than 5, leave the preceding digit unchanged.

• Example: 402.5367 rounded to 6 significant figures is 402.537; to 5 significant figures is 402.54.

Calculations with Significant Figures

• Addition and Subtraction: The result should have the same number of decimal places as the measurement with the least decimal places.

• Multiplication and Division: The result should have the same number of significant figures as the measurement with the least significant figures.

• Example (Addition): 2.987 + 0.23 + 5.0000 = 8.217 (rounded to 2 decimal places: 8.22)

• Example (Multiplication): $(2.34 \times 45.779) / 0.0344 = 3113.42441$ (rounded to 3 significant figures: 3110)

Scientific Notation

Purpose and Format

Scientific notation is used to express very large or very small numbers conveniently and to clearly indicate the number of significant figures.

• Format: $a \times 10^n$, where $1 \leq a < 10$ and $n$ is an integer.

• Examples:

  • 8200 = $8.2 \times 10^3$ (2 significant figures)

  • 8.20 × $10^3$ (3 significant figures)

  • 8.200 × $10^3$ (4 significant figures)

Additional info: The above notes provide foundational knowledge for measurement and data handling in General Chemistry, including the use of SI units, significant figures, and scientific notation, which are essential for accurate experimental work and reporting.