Matter: States, Composition, Changes, and Scientific Notation — Quick Review

States of matter

• Solids: retain shape regardless of container.
• Liquids: take container shape, keep volume; flow.
• Gases: fill container; take shape and volume of container; have large spaces between particles; highly compressible.
• Compressibility:
  • Solids and liquids: essentially incompressible.
  • Gases: compressible (lots of space between particles).

Composition and substance types

• Start by deciding: pure substance or mixture.
• If pure:
  • Is it an element or a compound?
• From the lecture cues:
  • If it says it’s only one kind of atom (e.g., helium), it’s an element.
• Key definitions from the notes:
  • Elements can exist as molecules (e.g., $H<em>2$, $O</em>2$) or as atoms.
  • All compounds are molecules because they contain two or more elements.
  • Therefore, compounds are molecules; not all elements are molecules.
  • Example: $H_2O$ is a compound.
• Distinguishing example with formulas:
  • If the left-side formula and the right-side formula are the same (e.g., $H<em>2O ightleftharpoons H</em>2O$), this is a physical change.
  • If the left and right formulas are different (e.g., $H<em>2 + O</em>2 <br /> ightarrow H<em>2O$ or $H</em>2O <br /> ightarrow H<em>2O</em>2$ depending on context), this is a chemical change.
  • State changes do not affect the classification: a physical change can involve a state change but the identity (formula) remains the same.

Physical vs chemical changes (summary)

• Physical change: identity remains the same; same chemical formula on both sides.
• Chemical change: identity changes; new substances formed; different formulas on products side.

Scientific notation basics

• Standard form concept: any number N can be written as $N = a \times 10^{n}$ where mantissa $a$ satisfies 1 \le a < 10.
• Converting standard to scientific notation:
  • Move the decimal point until the mantissa is between 1 and 9.
  • The exponent n reflects how many places you moved the decimal:
  • moving the decimal to the left yields a positive exponent,
  • moving it to the right yields a negative exponent.
• Examples from lecture:
  • $2600 = 2.6\times 10^{3}$
  • $0.031 = 3.1\times 10^{-2}$
• Converting back (scientific to standard): move the decimal according to the exponent (positive moves digits to the left, negative moves digits to the right).
• ALEKS-specific note:
  • If the prompt asks for scientific notation, ensure the mantissa is between 1 and 9 (i.e., the number should be written with a single-digit integer part before the decimal).
• Practical tip:
  • Some systems check input digit-for-digit; include required leading zeros or formatting exactly as requested.

Quick study tips for last-minute review

• Use the study sheets and pair related concepts (e.g., physical vs chemical changes) on the same page.
• Practice conversions between standard and scientific notation until you can do them quickly and accurately.
• Review examples of pure substances vs mixtures, and element vs compound, with emphasis on formula and identity.