Chemistry and Measurement Notes

Numbers in Chemistry

• Numbers are crucial in chemistry.

• Many topics are quantitative.

• Numbers can be very large or very small.

• Scientific notation simplifies writing these numbers.

Measurement

• Every measurement includes a number and a unit.

• The number is meaningless without the unit.

Scientific Notation

• Used for very small and very large numbers.

• A number is written as a coefficient multiplied by 10 raised to a power: $y \times 10^x$, where:

  • $y$ = coefficient (between 1 and 10)

  • $x$ = exponent (any positive or negative whole number)

• Numbers with positive exponents ($10^x$) are decimal numbers greater than one.

• Numbers with negative exponents ($10^{-x}$) are decimal numbers less than one.

Converting to Scientific Notation

1. Move the decimal point to get a number between 1 and 10.

2. Multiply by $10^x$, where $x$ = the number of places the decimal was moved. If moved:

   • Left, $x$ is positive.

   • Right, $x$ is negative.

Converting from Scientific Notation

• If the exponent $x$ is positive, move the decimal point $x$ places to the right.

• If the exponent $x$ is negative, move the decimal point $x$ places to the left.

Units of the Metric System

• Base units:

  • Mass: kilogram (kg)

  • Length: meter (m)

  • Time: second (s or sec)

  • Temperature: degrees Celsius (°C) or Kelvins (K)

  • Amount of a substance: mole (mol)

  • Volume: cubic centimeter (cc or cm3) or milliliter (mL)

• Prefixes are used for very large and very small numbers and indicate if the unit is larger or smaller than the base unit.

Mass and Length

• Mass: Amount of material in an object, base unit is gram (g).

  • 1 kilogram (kg) = 1,000 grams (g)

  • 1 milligram (mg) = 0.001 grams (g)

• Length: Distance, base unit is meter (m).

  • 1 kilometer (km) = 1,000 meters (m)

  • 1 millimeter (mm) = 0.001 meters (m)

  • 1 centimeter (cm) = 0.01 meters (m)

Temperature

• Formulas:

  • $°C = (°F – 32) \frac{5}{9}$

  • $°F = (°C) \frac{9}{5} + 32$

  • $K = °C + 273.15$

  • $°C = K - 273.15$

• Fahrenheit (°F):

  • 32°F Freezing H2O

  • 212°F Boiling H2O

• Celsius (°C):

  • 0°C Freezing H2O

  • 100°C Boiling H2O

• Kelvin (K):

  • 273 K Freezing H2O

  • 373 K Boiling H2O

Volume

• A derived unit from length ($m \times m \times m = m^3$).

• Common units: Liter (L) and milliliter (mL).

• 1 mL = 1 cubic centimeter (cm3).

Density

• Formula: $Density = \frac{Mass}{Volume}$

• Typical units: g/mL or g/cm3.

Significant Figures

• Exact numbers: Result from counting or are part of a definition.

• Inexact numbers: Result from a measurement and contain some uncertainty.

Rules for Determining Significant Figures

1. All nonzero digits are significant.

2. A zero counts as a significant figure when it occurs:

   • Between two nonzero digits.

   • At the end of a number with a decimal place.

3. A zero does not count as a significant figure when it occurs:

   • At the beginning of a number.

   • At the end of a number that does not have a decimal.

Rules for Calculations

• Multiplication and Division: The answer has the same number of significant figures as the original number with the fewest significant figures.

• Addition and Subtraction: The answer has the same number of decimal places as the original number with the fewest decimal places.

• Rounding:

  • If the first digit to be dropped is between 0 and 4, drop it and all remaining digits.

  • If the first digit to be dropped is between 5 and 9, round up the last digit to be retained by adding 1.

Conversions

• Conversion factor: A term that converts a quantity in one unit to a quantity in another unit.

• Factor-label method: Using conversion factors to convert a quantity in one unit to a quantity in another unit, making sure all unwanted units cancel.

Density

• Formula: $density = \frac{mass}{volume}$

• Density as a conversion factor:

  • To convert volume to mass: $mL \times \frac{g}{mL} = g$

  • To convert mass to volume: $g \times \frac{mL}{g} = mL$

Specific Gravity

• Formula: $specific \ gravity = \frac{density \ of \ a \ substance \ (g/mL)}{density \ of \ water \ (g/mL)}$

• Unitless.

• The specific gravity of a substance is approximately equal to its density since the density of water is ~1 g/mL.

Energy

• Energy: The capacity to do work or transfer heat.

  • Work: Energy transferred when a force exerted on an object causes a displacement of that object.

  • Heat: Energy used to cause the temperature of an object to increase.

Forms of Energy

• Kinetic energy (KE):

  • Energy of motion or movement.

  • Formula: $KE = \frac{1}{2} m v^2$

• Potential energy:

  • Energy that is waiting to happen.

  • Depends on the relative position of an object compared to other objects.

  • Stored in the chemical bonds that make up substances.