Mathematical and Computational Models - Revision history

Conrad: Remove the Rows section (anchor names are documented on Template:Rt)

2026-10-25T21:52:16Z

Remove the Rows section (anchor names are documented on Template:Rt)

Conrad: Row anchors as zero-height blocks above the image, so a row link shows the whole table

2026-10-25T21:41:10Z

Row anchors as zero-height blocks above the image, so a row link shows the whole table

Conrad: Show the official table image instead of a wikitext copy; row anchors now land on the image

2026-10-25T21:39:48Z

Show the official table image instead of a wikitext copy; row anchors now land on the image

Conrad: Make the Regents Exam Questions table scroll sideways on narrow screens instead of widening the page

2026-10-25T21:31:23Z

Make the Regents Exam Questions table scroll sideways on narrow screens instead of widening the page

Conrad: Chemistry reference tables (2025 Edition): new reference table page

2026-10-25T19:50:34Z

Chemistry reference tables (2025 Edition): new reference table page

New page

{{Chemreftable
|name=Mathematical and Computational Models
|prev=Selected Ions Forming Aqueous Solutions
|next=Mathematical Relationships
|desc=Mathematical and Computational Models from the NYS Chemistry Reference Tables (2025 Edition): the combined gas law, the heat equations q = mc delta T, q = mHf and q = mHv, the parts-per-million formula, n = MV for molarity, and the qualitative Coulombic force relationship, each with its variables. Supports HS-PS1-9, HS-PS3-1, HS-PS1-10 and HS-PS3-5.
}}
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"
! Equations !! Variables
|- id="combined-gas-law"
| style="text-align:center;" | ''P''1''V''1''T''1 = ''P''2''V''2''T''2
| ''P'' = pressure ''V'' = volume ''T'' = temperature
|- id="heat"
| style="text-align:center;" | ''q'' = ''mc''Δ''T'' ''q'' = ''mH''f ''q'' = ''mH''v
| ''q'' = heat ''m'' = mass ''c'' = specific heat capacity Δ''T'' = change in temperature ''H''f = heat of fusion ''H''v = heat of vaporization
|- id="ppm"
| style="text-align:center;" | ppm = mass of solutemass of solution × 1 000 000
| ppm = parts per million
|- id="molarity"
| style="text-align:center;" | ''n'' = ''MV''
| ''n'' = moles ''M'' = molarity ''V'' = volume
|- id="coulombic-force"
| style="text-align:center;" | ''F'' ∝ ''q''1''q''2''d''2 *qualitative analysis
| ''F'' = coulombic force ''q'' = charge ''d'' = distance of separation
|}

== What the equations table shows ==
'''Combined gas law.''' ''P''1''V''1/''T''1 = ''P''2''V''2/''T''2 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 [[Mathematical Relationships#temperature|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'' = ''mc''Δ''T'' 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 [[Mathematical Relationships#mole|molar mass]], and a volume in milliliters takes the milli- prefix from [[Selected Metric Prefixes]].

'''Coulombic force.''' ''F'' ∝ ''q''1''q''2/''d''2 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.

{| class="wikitable" style="width:100%; text-align:center"
! style="padding: 0.5em 1.5em;" | Exam
! style="padding: 0.5em 1.5em;" | Cluster
! style="padding: 0.5em 1.5em;" | Question
! style="padding: 0.5em 1.5em;" | Standard
! style="padding: 0.5em 1.5em;" | Row
|-
| rowspan="3" style="background-color:white;" | [[August 2026 Chemistry Exam|August 2026 Chemistry Regents]]
| style="background-color:white;" | [[Questions:The ABCs of Ultraviolet Radiation|The ABCs of Ultraviolet Radiation]]
| style="background-color:white;" | [[Questions:The ABCs of Ultraviolet Radiation#q3|Question 28]]
| style="background-color:white;" | [[HS-PS1-10]]
| style="background-color:white;" | ppm
|-
| style="background-color:white;" | [[Questions:Parade of Balloons|Parade of Balloons]]
| style="background-color:white;" | [[Questions:Parade of Balloons#q3|Question 41]]
| style="background-color:white;" | [[HS-PS1-9]]
| style="background-color:white;" | Combined gas law
|-
| style="background-color:white;" | [[Questions:Parade of Balloons|Parade of Balloons]]
| style="background-color:white;" | [[Questions:Parade of Balloons#q4|Question 42]]
| style="background-color:white;" | [[HS-PS1-9]]
| style="background-color:white;" | Combined gas law
|-
| rowspan="5" style="background-color:white;" | [[June 2026 Chemistry Exam|June 2026 Chemistry Regents]]
| style="background-color:white;" | [[Questions:Urban Heat Islands|Urban Heat Islands]]
| style="background-color:white;" | [[Questions:Urban Heat Islands#q1|Question 19]]
| style="background-color:white;" | [[HS-PS3-1]]
| style="background-color:white;" | Heat equations
|-
| style="background-color:white;" | [[Questions:Urban Heat Islands|Urban Heat Islands]]
| style="background-color:white;" | [[Questions:Urban Heat Islands#q2|Question 20]]
| style="background-color:white;" | [[HS-PS3-1]]
| style="background-color:white;" | Heat equations
|-
| style="background-color:white;" | [[Questions:Balloon Arches|Balloon Arches]]
| style="background-color:white;" | [[Questions:Balloon Arches#q1|Question 23]]
| style="background-color:white;" | [[HS-PS1-9]]
| style="background-color:white;" | Combined gas law
|-
| style="background-color:white;" | [[Questions:Balloon Arches|Balloon Arches]]
| style="background-color:white;" | [[Questions:Balloon Arches#q4|Question 26]]
| style="background-color:white;" | [[HS-PS1-9]]
| style="background-color:white;" | Combined gas law
|-
| style="background-color:white;" | [[Questions:Clock Reaction|Clock Reaction]]
| style="background-color:white;" | [[Questions:Clock Reaction#q5|Question 32]]
| style="background-color:white;" | [[HS-PS1-10]]
| style="background-color:white;" | n = MV
|}

← Older revision		Revision as of 21:52, 25 October 2026
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	'''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]].		'''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 ==		== Regents Exam Questions ==

@@ 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]].
-<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)]]
+<div id="combined-gas-law"></div><div id="heat"></div><div id="ppm"></div><div id="molarity"></div><div id="coulombic-force"></div>
 == What the equations table shows ==

@@ Line 40: / Line 40: @@
 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.
 {| class="wikitable" style="width:100%; text-align:center"
 ! style="padding: 0.5em 1.5em;" | Exam
@@ Line 89: / Line 90: @@
 | style="background-color:white;" | n = MV
 |}