Difference between revisions of "Mathematical and Computational Models"
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Revision as of 17:31, 25 October 2026
| ⇱ All Chemistry Reference Tables (2025 Edition) | |
| ← Selected Ions Forming Aqueous Solutions | Mathematical Relationships → |
The Mathematical and Computational Models table from the Reference Tables for Physical Science: Chemistry (2025 Edition) is the equation sheet: five rows, each with an equation (or a set of equations) and the meaning of its variables. Each row belongs to a different standard, so links from the standards pages point at individual rows: the combined gas law supports HS-PS1-9; the heat equations HS-PS3-1; parts per million and n = MV HS-PS1-10 (n = MV also serves titration problems in HS-PS1-11); and the Coulombic force relationship HS-PS3-5, as well as the qualitative reasoning about electrical forces in HS-PS1-1, HS-PS1-3 and HS-PS2-6.
| Equations | Variables |
|---|---|
| P1V1T1 = P2V2T2 | P = pressure V = volume T = temperature |
| q = mcΔT q = mHf q = mHv |
q = heat m = mass c = specific heat capacity ΔT = change in temperature Hf = heat of fusion Hv = heat of vaporization |
| ppm = mass of solutemass of solution × 1 000 000 | ppm = parts per million |
| n = MV | n = moles M = molarity V = volume |
| F ∝ q1q2d2 *qualitative analysis |
F = coulombic force q = charge d = distance of separation |
What the equations table shows
Combined gas law. P1V1/T1 = P2V2/T2 relates the pressure, volume and temperature of a fixed amount of gas before and after a change; holding one variable constant gives the relationship between the other two. Temperature must be in kelvin, so a calculation usually starts with the K = °C + 273.15 conversion. HS-PS1-9's assessment boundary covers the relationships among the variables, not the names of the individual gas laws.
Heat. q = mcΔT gives the heat absorbed or released when a substance changes temperature without changing phase; q = mHf the heat for melting or freezing; q = mHv the heat for boiling or condensing. Specific heat capacities and heats of fusion and vaporization are not on the 2025 tables (the 2011 edition's Table B gave water's 4.18 J/g·K, 334 J/g and 2260 J/g); the values a question needs are supplied in the cluster, and masses in kilograms or energies in kilojoules need the Selected Metric Prefixes.
Parts per million. ppm = (mass of solute ÷ mass of solution) × 1 000 000. HS-PS1-10's clarification statement lists ppm, molarity and percent by mass as the ways to express concentration, but only ppm and molarity are on the 2025 tables; a percent-by-mass calculation (August 2026 Q38) has to be done without a formula from the tables.
Molarity. n = MV: moles of solute equal molarity times volume in liters. It is the 2011 edition's M = n/V rearranged. Converting the moles to grams takes the molar mass, and a volume in milliliters takes the milli- prefix from Selected Metric Prefixes.
Coulombic force. F ∝ q1q2/d2 is marked *qualitative analysis: there is no constant, so it is used to compare forces rather than calculate them. Larger charges mean a stronger attraction or repulsion; greater separation means a weaker one. It is the model behind periodic trends in HS-PS1-1 (a larger nuclear charge pulls harder on the outer electrons; a greater distance pulls less), the strength of electrical forces between particles in HS-PS1-3 and HS-PS2-6, and the interactions in HS-PS3-5.
Regents Exam Questions
Released Regents questions that cannot be answered without this table, listed by exam. Each link opens the question with its answer key; the standard is the one the question assesses.
| Exam | Cluster | Question | Standard | Row |
|---|---|---|---|---|
| August 2026 Chemistry Regents | The ABCs of Ultraviolet Radiation | Question 28 | HS-PS1-10 | ppm |
| Parade of Balloons | Question 41 | HS-PS1-9 | Combined gas law | |
| Parade of Balloons | Question 42 | HS-PS1-9 | Combined gas law | |
| June 2026 Chemistry Regents | Urban Heat Islands | Question 19 | HS-PS3-1 | Heat equations |
| Urban Heat Islands | Question 20 | HS-PS3-1 | Heat equations | |
| Balloon Arches | Question 23 | HS-PS1-9 | Combined gas law | |
| Balloon Arches | Question 26 | HS-PS1-9 | Combined gas law | |
| Clock Reaction | Question 32 | HS-PS1-10 | n = MV |