Difference between revisions of "Mathematical and Computational Models"

Revision as of 17:39, 25 October 2026

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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.

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 = mH_f the heat for melting or freezing; q = mH_v 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.

Rows

A link or an {{Rt}} chip (Template:Rt) can point at one equation or constant with these anchors; each one lands on the table above:

combined-gas-law – Combined gas law
heat – Heat equations (q = mcΔT, q = mH_f, q = mH_v)
ppm – ppm
molarity – n = MV
coulombic-force – Coulombic force

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

@@ Line 7: / Line 7: @@
 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]].
-{| class="wikitable"
+<span id="combined-gas-law"></span><span id="heat"></span><span id="ppm"></span><span id="molarity"></span><span id="coulombic-force"></span>[[File:Mathematical and Computational Models.png|680px|class=img-fluid|alt=Mathematical and Computational Models from the Chemistry Reference Tables (2025 Edition)]]
-! Equations !! Variables
-|- id="combined-gas-law"
-| style="text-align:center;" | <span style="display:inline-block;vertical-align:middle;text-align:center;line-height:1.25;"><span style="display:block;border-bottom:1px solid currentColor;padding:0 3px;">''P''<sub>1</sub>''V''<sub>1</sub></span><span style="display:block;padding:0 3px;">''T''<sub>1</sub></span></span> = <span style="display:inline-block;vertical-align:middle;text-align:center;line-height:1.25;"><span style="display:block;border-bottom:1px solid currentColor;padding:0 3px;">''P''<sub>2</sub>''V''<sub>2</sub></span><span style="display:block;padding:0 3px;">''T''<sub>2</sub></span></span>
-| ''P'' = pressure<br>''V'' = volume<br>''T'' = temperature
-|- id="heat"
-| style="text-align:center;" | ''q'' = ''mc''Δ''T''<br>''q'' = ''mH''<sub>f</sub><br>''q'' = ''mH''<sub>v</sub>
-| ''q'' = heat<br>''m'' = mass<br>''c'' = specific heat capacity<br>Δ''T'' = change in temperature<br>''H''<sub>f</sub> = heat of fusion<br>''H''<sub>v</sub> = heat of vaporization
-|- id="ppm"
-| style="text-align:center;" | ppm = <span style="display:inline-block;vertical-align:middle;text-align:center;line-height:1.25;"><span style="display:block;border-bottom:1px solid currentColor;padding:0 3px;">mass of solute</span><span style="display:block;padding:0 3px;">mass of solution</span></span> × 1&nbsp;000&nbsp;000
-| ppm = parts per million
-|- id="molarity"
-| style="text-align:center;" | ''n'' = ''MV''
-| ''n'' = moles<br>''M'' = molarity<br>''V'' = volume
-|- id="coulombic-force"
-| style="text-align:center;" | ''F'' ∝ <span style="display:inline-block;vertical-align:middle;text-align:center;line-height:1.25;"><span style="display:block;border-bottom:1px solid currentColor;padding:0 3px;">''q''<sub>1</sub>''q''<sub>2</sub></span><span style="display:block;padding:0 3px;">''d''<sup>2</sup></span></span><br>*qualitative analysis
-| ''F'' = coulombic force<br>''q'' = charge<br>''d'' = distance of separation
-|}
 == What the equations table shows ==
@@ Line 36: / Line 19: @@
 '''Coulombic force.''' ''F'' ∝ ''q''<sub>1</sub>''q''<sub>2</sub>/''d''<sup>2</sup> 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]].
+== Rows ==
+A link or an <code><nowiki>{{Rt}}</nowiki></code> chip ([[Template:Rt]]) can point at one equation or constant with these anchors; each one lands on the table above:
+* <code>combined-gas-law</code> – Combined gas law
+* <code>heat</code> – Heat equations (''q'' = ''mc''Δ''T'', ''q'' = ''mH''<sub>f</sub>, ''q'' = ''mH''<sub>v</sub>)
+* <code>ppm</code> – ppm
+* <code>molarity</code> – ''n'' = ''MV''
+* <code>coulombic-force</code> – Coulombic force
 == Regents Exam Questions ==