Conservation Laws

Law of Conservation of Mass:

Mass is neither created nor destroyed during a chemical change. (Strictly speaking there is no measurable change.) For example, if we burn gasoline (octane) in air we will get carbon dioxide and water:

C₈H₁₈ + 12 1/2 O₂ 8 CO₂ + 9 H₂O

If we were to weigh (determine the mass) of the carbon and oxygen vs. the carbon dioxide and water we would find them to be identical - the masses are the same on both sides of the equation (that's why its called a chemical equation, the two sides are equal in mass). Looked at another way, if you count the atoms, the numbers of each kind of atom on each side are identical - so we can also say that atoms are conserved in chemical processes.

Law of Conservation of Energy:

Energy is neither created nor destroyed in chemical processes. The problem here of course is - What is energy? Energy is the capacity to do work. So what's work? Work occurs when an object (mass) is moved against a force. Some common forms of energy important to our study include:

• Kinetic Energy (KE) - energy due to motion. KE = 1/2 mv².
• Potential Energy (PE) - energy due to position.

Another form of energy we need to be familiar with is:

• Heat - energy transferred between objects because of a difference in temperature.
  • Heat vs. Temperature: heat tells us how much energy is held (can be transferred from) and object or given mass of stuff. Temperature on the other hand is a measure of the energy per particle in a sample of matter. Thus for a gas temperature is a measure of the average Kinetic Energy (KE) of the gas particles, while the amount of energy we must add to the gas to achieve this average KE is the heat.
  • Note that most energy eventually ends up as heat (ex.: burning gasoline to move a car - heat in exhaust, friction in tire deformation, braking, etc.) or work (car is moved against its inertia).

Note that these forms of energy are readily interconverted.

Composition of Matter

• Pure substances: have the same chemical composition regardless of origin and thoughout any sample. Pure substances can be of two types,
  • Elements are substances that cannot be broken down into simpler substances by chemical means. The elements are organized into the Periodic Table of the elements as seen below. We will come back and explore this table in detail later.
    • Note the symbols and numbers on the table.
    • The atomic number determines the element, and could stand in for the symbol and name.

• Compounds are substances composed of two or more chemical elements combined in definite proportions.

SI Units ("metric" system)

The metric system originated in the French Revolution as a rational system of measurements to rescue France from the chaos of pre-revolutionary measurements and thus prevent tax collectors from cheating.

Wanted to base system on "natural" universal standards. Thus for length they chose the size of the Earth: specifically the meter was defined as one ten-millionth (10^-7) of one quarter of the Earth's meridian* passing through Paris (the line along the "surface" of the Earth from the north pole though Paris to the equator). For mass the Kilogram was defined as the mass of a cube of water 0.1 meter on a side. Of course these are not convenient, so other standards were quickly created: the meter became the distance between two lines on a platinum-iridium bar stored in a vault in Paris, while the kilogram became a cylindrical mass of platinum-iridium alloy stored in the same vault.

Today the various units are defined by international agreement to give the SI (Systéme International) units:

• Length: the meter (m) is defined as the distance light travels in a vacuum in 1/299,792,458 sec. (Note that this is truly universal: in principle it can be determined by anyone, anytime, anywhere in the Universe. It also fixes the speed of light, c, as 299,792,458 m/s = 2.99792458 x 10⁸ m sec^-1)
• Mass: the kilogram (kg) however is still based on the International Prototype Kilogram in Paris and the derived standard kilogram standards held by governments around the world.
• Time: the second (s) is defined today as the duration of 9,192,631,770 periods of the radiation of two hyperfine levels of the ground state of the cesium 133 atom.
• Amount of substance: the mole (mol) is defined as the number of atoms in 0.012 kg (defined, so sig figs not restricted) of carbon 12 atoms. One mole = 6.022 x 10²³ particles.
• Temperature: the kelvin (K) is defined as 1/273.15 of the thermodynamic temperature of the triple point of water.

Prefixes:

Note Table 3.2 in your text (p 38). You should know and be able to interconvert the prefixes in the table below:

Prefix Symbol Magnitude kilo- k 103 base   100 deci- d 10-1 centi- c 10-2 milli- m 10-3 micro- (or mc) 10-6 nano- n 10-9

Other common prefixes which you should be familiar with but do not need to memorize include: tera- (T, 10¹²), giga- (G, 10⁹), mega- (M, 10⁶), pico- (p, 10^-12), and fempto- (f, 10^-15).

Memorize: 1 mL = 1 cm³; 1 inch = 2.54 cm; 1 liter is about 1 quart; density of water = 1 g/mL; 0° C = 32 °F, 100°C = 212 °F, -40 °C = -40 °F

Dimensional (Unit) Analysis and Problem Solving

A convenient check on your work, or even a way to determine the best approach to a problem, is to use dimensional analysis. This simply means to include all of the units for each factor in an equation, and then to check to see that the units on both sides of the equation are equal.

For example, how long is a one foot ruler? Know conversion for cm to inches: 2.54 cm = 1 inch (no sig figs, defined ) [ans. = 30.48 cm]

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Last modified 1 September 2009