Exam 1 Chem
The Periodic Table
Reading the Periodic Table
Atomic Number (Z): of protons in an atom, defines the element. Usually at the top of the element symbol.
Atomic Mass (Average Atomic Weight): Weighted average of the masses of an element's isotopes. Usually at the bottom of the symbol.
Example: The element with 27 protons is Cobalt (Co), and its atomic mass is approximately 58.933194 amu.
Periods: Horizontal rows, indicate the number of electron shells.
Groups (Families): Vertical columns, elements in the same group have similar chemical properties due to the same number of valence electrons.
Classification of Elements
Metals: Generally good conductors of heat and electricity, malleable, ductile, typically characterized by forming positive ions.
Example: Sodium (Na)
Nonmetals: Generally poor conductors of heat and electricity, often brittle (if solid), typically characterized by forming negative ions or covalent bonds.
Example: Oxygen (O)
Metalloids (Semimetals): Have properties intermediate between metals and nonmetals, often semiconductors.
Example: Silicon (Si)
Elements Liquid at Room Temperature
The primary elements that are liquid at standard room temperature (20-25^ ext{o} ext{C} ) are Bromine (Br) and Mercury (Hg).
Important Groups and Typical Ionic Forms
Group 1: Alkali Metals (e.g., Li, Na, K)
Highly reactive metals, typically form +1 ions (lose one electron).
Application: An unidentified element found to be in the form of an ion with a charge of +1, and not a Transition Metal, is most likely an Alkali Metal.
Group 2: Alkaline Earth Metals (e.g., Be, Mg, Ca)
Reactive metals, typically form +2 ions (lose two electrons).
Group 17: Halogens (e.g., F, Cl, Br)
Highly reactive nonmetals, typically form -1 ions (gain one electron).
Group 18: Noble Gases (e.g., He, Ne, Ar)
Very unreactive (inert) due to a full outer electron shell, do not typically form ions.
Transition Metals: (Groups 3-12)
Often form multiple different positive ions (e.g., Fe{}^{2+}, Fe{}^{3+}).
The Scientific Method
Observation: Noticing a phenomenon or problem.
Example Fictitious Observation: Every Tuesday precisely at sunset, all the pigeons in my neighborhood start glowing with a faint purple aura for exactly five minutes.
Question: Asking why or how something occurs.
Example Question: Why do the neighborhood pigeons glow purple at sunset on Tuesdays?
Hypothesis: A testable explanation or prediction for an observation. (If X, then Y will happen).
Example Hypothesis: If pigeons consume a specific type of rare, bioluminescent berry that only ripens on Tuesdays, then they will glow purple when exposed to the last rays of sunlight.
Note: A hypothesis is an educated guess or proposed explanation, not yet a scientific theory. A scientific theory is a well-substantiated explanation acquired through the scientific method and repeatedly tested and confirmed through observation and experimentation, often encompassing many related hypotheses. A single experiment confirming a hypothesis does not elevate it to the status of a theory.
Application: If an experiment agreed with the hypothesis above regarding glowing pigeons, the hypothesis would not become a theory. This is because a single experiment, even if it supports the hypothesis, is not sufficient for it to be considered a well-substantiated theory that has been repeatedly tested and confirmed through extensive observation and experimentation.
Experimentation: Designing and conducting tests to prove or disprove the hypothesis.
Example Experiment: To test the glowing pigeon hypothesis, collect a sample of the glowing pigeons’ droppings on a Tuesday evening and analyze them for traces of the hypothesized bioluminescent berry. Simultaneously, compare it to droppings collected from non-glowing pigeons on other days.
Independent Variable: The factor intentionally changed by the experimenter.
Dependent Variable: The factor observed or measured that may change in response to the independent variable.
Control Group: A baseline for comparison, where the independent variable is not applied.
Analysis: Interpreting the data collected during the experiment.
Conclusion: Determining whether the hypothesis was supported or rejected based on the data.
If the hypothesis is supported, it gains credibility but still requires further testing and replication by others.
If the hypothesis is rejected, this also contributes to scientific progress by ruling out a potential explanation.
Application: If the experiment disagreed with the hypothesis, this outcome would help scientific progress by ruling out a potential explanation for the glowing pigeons. The next step as a scientist would be to revise the original hypothesis or formulate a new one based on the new findings, and then design further experiments to test it.
Forms of Matter
Pure Substance: A substance with a uniform and definite composition and distinct properties throughout. Pure substances include elements and compounds.
Element: A pure substance consisting of only one type of atom (e.g., O₂, Fe, H₂).
Cannot be broken down into simpler substances by chemical means.
Explanation: It is pure because its composition is uniform and definite, as it consists solely of one type of atom defining its unique properties.
Compound: A pure substance formed when two or more different elements are chemically bonded together in fixed proportions (e.g., H₂O, NaCl, CO₂).
Can be broken down into simpler substances (elements) by chemical means.
Explanation: It is pure because its composition is also uniform and definite, as the elements are chemically bonded in fixed ratios, giving the compound distinct properties different from its constituent elements.
Example of a Compound: Table salt (sodium chloride, NaCl) is a Pure Substance and a Compound.
It is a Pure Substance because it has a uniform and definite composition, consisting of sodium and chlorine chemically bonded together in fixed proportions, and it exhibits distinct properties throughout.
It is a Compound because it is formed when two or more different elements, sodium (Na) and chlorine (Cl), are chemically bonded together in a fixed ratio, and it can be broken down into these simpler elements by chemical means.
Mixture: A combination of two or more substances that are not chemically bonded.
Components retain their individual properties.
Can be separated by physical means.
Homogeneous Mixture (Solution): Components are uniformly distributed throughout, appears as a single phase (e.g., saltwater, air, brass).
Individual components are not visible.
Heterogeneous Mixture: Components are not uniformly distributed and can often be visibly distinguished (e.g., sand and water, salad, oil and vinegar).
Individual components are visible.
Physical and Chemical Changes
Physical Change: A change in the form or appearance of a substance, but not its chemical composition.
No new substances are formed.
Often easily reversible.
Indicators: Changes in state (melting, freezing, boiling, condensation, sublimation), changes in size or shape (cutting, bending), dissolving.
Example: Ice melting into water (still H₂O).
Chemical Change (Chemical Reaction): A change where a new substance with different chemical properties is formed.
Involves the breaking and forming of chemical bonds.
Often difficult to reverse.
Indicators: Formation of a gas (bubbles) not from boiling, formation of a precipitate (solid from liquid solution), color change, significant temperature change (heat absorbed/released), emission of light or sound.
Example: Burning wood (wood turns to ash and smoke).
Scientific Notation
Purpose: To express very large or very small numbers concisely.
Format: M \times 10^n
M (mantissa) is a number greater than or equal to 1 and less than 10 (decimal after the first non-zero digit).
n (exponent) is an integer indicating the number of places the decimal point was moved.
Converting a normal number to scientific notation:
Move the decimal point until there is only one non-zero digit to its left.
Count the number of places the decimal was moved; this is n.
If the decimal moved left, n is positive; if it moved right, n is negative.
Example: 345000 = 3.45 \times 10^5 (decimal moved 5 places left)
Example: 0.0000072 = 7.2 \times 10^{-6} (decimal moved 6 places right)
Example: 73500 = 7.35 \times 10^4
Example: 0.0000873 = 8.73 \times 10^{-5}
Converting scientific notation to a normal number:
If n is positive, move the decimal point n places to the right.
If n is negative, move the decimal point n places to the left.
Example: 1.23 \times 10^4 = 12300
Example: 8.9 \times 10^{-3} = 0.0089
Metric Units and Conversion Factors
Base Units:
Length: meter (m)
Mass: gram (g)
Volume: liter (L)
Time: second (s)
Common Prefixes:
kilo- (k): 10^3 (1 km = 1000 m)
centi- (c): 10^{-2} (1 cm = 0.01 m, or 1 m = 100 cm)
milli- (m): 10^{-3} (1 mm = 0.001 m, or 1 m = 1000 mm)
Conversion Strategy (Dimensional Analysis): Use conversion factors as fractions to cancel units until the desired unit is obtained.
Example: Convert 2.5 meters to millimeters:
2.5 \text{ m} \times \frac{1000 \text{ mm}}{1 \text{ m}} = 2500 \text{ mm}Example: Convert 3 grams to kilograms:
3 \text{ g} \times \frac{1 \text{ kg}}{1000 \text{ g}} = 0.003 \text{ kg}Example: Convert 2 cubic meters to cubic centimeters (cm³):
2 \text{ m}^3 \times (\frac{100 \text{ cm}}{1 \text{ m}})^3 = 2 \text{ m}^3 \times \frac{1,000,000 \text{ cm}^3}{1 \text{ m}^3} = 2,000,000 \text{ cm}^3Example: What is the volume of a 7 cm cube in Liters (L)?
Volume in cm³: (7 \text{ cm})^3 = 343 \text{ cm}^3
Convert to mL: 343 \text{ cm}^3 = 343 \text{ mL} (since 1 \text{ cm}^3 = 1 \text{ mL})
Convert to L: 343 \text{ mL} \times \frac{1 \text{ L}}{1000 \text{ mL}} = 0.343 \text{ L}
Complex Dimensional Analysis Example (Nonsense Units): A bubble has 3 bloops (bl), 6 glops (gl), and 7 flumps (fl). How much gobbledygook (gg) is there in the bubble? Note that 1 \text{ gg} = 1 (\text{bl}\cdot\text{fl})/\text{gl}.
Calculation: \frac{(3 \text{ bl} \times 7 \text{ fl})}{6 \text{ gl}} = \frac{21 \text{ bl}\cdot\text{fl}}{6 \text{ gl}} = 3.5 \text{ gg}
Analog Measurements
Making Analog Measurements: Read the major markings, then estimate one digit beyond the smallest marked increment.
Recording Digit Precision: The last digit recorded in an analog measurement is always an estimated digit.
Example: If a ruler has markings every millimeter (0.1 cm), you can estimate to the nearest tenth of a millimeter (0.01 cm).
If an object ends exactly on the 5.2 cm mark, you might record it as 5.20 cm (estimating the last zero).
If it's halfway between 5.2 and 5.3 cm, you might record it as 5.25 cm.
Resulting measurements have significant figures determined by the instrument's precision.
Significant Figures
Rules for Determining Significant Figures:
Non-zero digits are always significant. (e.g., 301 has 3 sig figs)
Zeros between non-zero digits are significant. (e.g., 301 has 3 sig figs)
Leading zeros (zeros before non-zero digits) are NOT significant. They only indicate the position of the decimal point. (e.g., 0.0052 has 2 sig figs)
Trailing zeros (zeros at the end of the number) are significant ONLY if the number contains a decimal point. (e.g., 250.00 has 5 sig figs; 250 would have 2 sig figs, but this can be ambiguous without a decimal point.)
Examples:
0.0052: 2 significant figures (leading zeros are not significant)
301: 3 significant figures (non-zero digits and zero between them are significant)
250.00: 5 significant figures (trailing zeros after a decimal point are significant)
Chemical Symbols, Mass Number, and Charge
Standard Notation: \sideset{^{A}}{_{Z}} \text{X}^C
X: Chemical symbol of the element (e.g., C for Carbon, O for Oxygen).
A (Mass Number): Total number of protons and neutrons in the nucleus. (Sum of Z and N).
Z (Atomic Number): Number of protons in the nucleus. (Also the number of electrons in a neutral atom).
C (Charge): Electrical charge of the ion. (Positive for cations, negative for anions).
Identifying Protons, Neutrons, and Electrons:
Number of Protons (Z): Always equal to the atomic number.
Number of Neutrons (N): N = A - Z
Number of Electrons (e⁻):
For a neutral atom: e^{-} = Z
For an ion: e^{-} = Z - C (where C is the charge, e.g., for \text{O}^{2-}, C = -2, so e^{-} = Z - (-2) = Z+2)
Example: \sideset{^{12}}{_{6}} \text{C} (neutral Carbon-12)
Protons: 6
Neutrons: 12 - 6 = 6
Electrons: 6
Example: \sideset{^{23}}{_{11}} \text{Na}^{+} (Sodium ion)
Protons: 11
Neutrons: 23 - 11 = 12
Electrons: 11 - (+1) = 10
Example: A carbon atom (\sideset{^{12}}{{6}} \text{C}) with one electron removed forms the ion \sideset{^{12}}{{6}} \text{C}^{+} (Protons: 6, Neutrons: 6, Electrons: 6-1 = 5).
Example: For a phosphorus atom (P) with a charge of -3 (\sideset{^{31}}{_{15}} \text{P}^{3-}), the number of electrons is Z - C = 15 - (-3) = 15 + 3 = 18 electrons.
Example: For the made-up element Unrealium, \sideset{^{312}}{_{121}} \text{X}^{2+}:
Protons (Z): 121
Neutrons (N): A - Z = 312 - 121 = 191
Electrons (e⁻): Z - C = 121 - (+2) = 119
Isotopes and Average Atomic Mass
Isotopes: Atoms of the same element (same number of protons) that have different numbers of neutrons, and therefore different mass numbers.
Example: Carbon-12 (\sideset{^{12}}{{6}} \text{C}) and Carbon-14 (\sideset{^{14}}{{6}} \text{C})
Note on Mass Difference: If two isotopes of the same element have mass numbers of 44 and 48, the difference in mass (in units of amu) between them is 48 - 44 = 4 \text{ amu}.
Average Atomic Mass: The weighted average mass of all naturally occurring isotopes of an element. Found on the periodic table.
Calculating Average Atomic Mass: Average Atomic Mass = \Sigma (Fractional Abundance of Isotope i) \times (Mass of Isotope i)
Fractional abundance is the percentage abundance expressed as a decimal (e.g., 75% = 0.75).
Example: If an element has two isotopes:
Isotope A: Mass = mA, Abundance = pA
Isotope B: Mass = mB, Abundance = pB
Average Atomic Mass = (pA \times mA) + (pB \times mB)
Example: An unknown element has 3 isotopes with masses of 4 amu, 5 amu, and 6 amu. Their respective abundances are 75%, 15%, and 10%. The average mass of this element is:
(0.75 \times 4 \text{ amu}) + (0.15 \times 5 \text{ amu}) + (0.10 \times 6 \text{ amu})
= 3.00 \text{ amu} + 0.75 \text{ amu} + 0.60 \text{ amu} = 4.35 \text{ amu}