Chemistry Equations
List of Equations and their uses for Preliminary and HSC Chemistry
Table of Contents
Gibbs Free Energy
Formula: $\Delta G=\Delta HT\Delta S$
Question: Determine whether the chemical reaction is spontaneous
Procedure:
 Write equation
 Calculate change in enthalpy ($\Delta H$) for reaction
 Calculate change in entropy ($\Delta S$) for reaction
 Calculate Gibbs Free Energy ($G$) for equation
 If $G$ is positive, the reaction is not spontaneous. If $G$ is zero or negative, the reaction is spontaneous
Equilibrium Constant
Formula: $K_{eq}=\frac{[C]^{c}\cdot [D]^{d}}{[A]^{a}\cdot [B]^{b}}$
Question: Calculate the equilibrium constant.
Procedure:
 Write a balanced chemical equation
 Convert moles of gas to concentration if necessary ($c=\frac{n}{v}$)
 Draw ICE (Initial, Change, Equilibrium) Table^{1} if necessary
 Calculate $K_{eq}$ using equation
Question: Determine if the system is at equilibrium and, if not, which way it will shift.
Procedure:

The question will give you a value for $K_{eq}$ (or you might calculate it in a previous section)

Use the same procedure as above, but with $Q$ instead of $K_{eq}$

Compare $Q$ and $K_{eq}$:
a. If $Q=K_{eq},$ then the system is at equilibrium
b. If $Q<K_{eq},$ then the system will proceed in the FORWARD direction
c. If $Q>K_{eq},$ then the system will proceed in the REVERSE direction
Question: Calculate $K_p$
Procedure:
 Calculate mole fraction (no of moles/total moles of gas)
 Multiply mole fraction by total pressure
 Use equilibrium equation, substituting partial pressures for concentration
Question: Given the initial concentration and $pH$ of a compound, find $K_{eq}$ of the dissociation/hydrolysis of the ions.
Procedure:
 Write the dissociation equation of the compounds (if not already given)
 Calculate the number of $H^+$ ions from the $pH$ ($H^+ = log_{10}(pH)$)
 Draw ICE Table ^{1} with initial concentration as the initial of the compound
 Substitute the $H^+$ values of each ion (from part 2) in the table as the final equilibrium concentration
 Write $K_{eq}$ and substitute values
 Assume the $x$ in number $x$ is negligible (from equilibrium concentration of compound) and remove
 Solve.
Acid/Base Dissociation Constant
Formula: $K_a = \frac{[\ce{H3O+}][\ce{A}]}{HA}$
Question: What is the acid/base dissociation constant of {compound}?
Procedure:
 Write the equation for dissociation (reacting with water)
 Write dissociation expression of the compound
 Draw ICE table using the initial concentration given, and substitute the other values with $x$
 Using $pH/pOH,$ calcullate the number of $H^+$ or $OH^$ ions, and replace $x$ with this value
 Substitute numbers into dissociation expression
Question: Given the concentration and Ka find the pH of the solution.
Procedure:

Write the equation for the dissociation of compound (react with water)

Write dissociation expression of compound^{2}

Draw ICE table using the initial concentration given and substituting other values with ‘x’

Substitute into dissociation expression

Assume $x$ is negligible and delete the $x$

Simplify and solve to find $x$ (concentration of $H^+$ ions)

Substitute value of $x$ into formula to find pH ( $log[H^+]$ )
Strength of Acid/Base
Formula: $pK_a =log_{10}[K_a]$
Solubility Equilibrium
Formula: $K_{sp}=[A][B]$
Question: Compare solubility of salt in water and another solute with shared ion (common ion effect).
Procedure:

Write balanced solubility equation for dissociation of salt

Draw MICE table, with initial ratio of shared ion as concentration of solution

Substitute change with ‘x’

Substitute into solubility expression using the values from table

Assume that the x in (number +x) is negligible compared to original concentration and remove it

Solve equation using the Ksp
Question: Calculate solubility of compound/concentration of ions from Ksp.
Procedure:

Write balanced solubility equation for dissociation of salt

Write Ksp equation

Substitute ‘x’ into concentrations

Solve using Ksp.
Question: Calculate molar solubility of the compound from Ksp.
Procedure:

Write balanced solubility equation for the dissociation of the salt

Determine concentration for the ions and use mole ratios to substitute as ‘s’

Write equilibrium expression and substitute ‘s’ into value, solve to find ‘s’
Question: When two solutions are mixed, will a precipitate form, given Ksp of precipitate.
Procedure:

Write separate dissociation equations for both solutions

Calculate the number of moles in each of the solutions for the volume given

Find new concentration of the precipitate forming ions (moles/new volume)

Substitute new concentrations into Qsp

Compare with Ksp to assess if precipitate forms
Question: Give Ksp values, which compound precipitates first?
Procedure:

Write separate dissociation equations for both compounds

Write Ksp equation and substitute ‘x’ for concentrations

Solve for ‘x’ using given Ksp

Repeat for the other compound

Compare values of x, lower volume precipitates first
Question: Given Ksp and number of moles of reactants in mixture, calculate concentration of ions at equilibrium.
Procedure:

Write equation of both reactant solutions to form precipitate

Find limiting reagent

Find moles of excess reagent (total moles – moles of limiting reagent)

Write Ksp equation

Rearrange equation as [ions] = Ksp / [other ions]

Substitute given Ksp values and concentration of excess reagent (using number of moles from step 3)

Solve for concentration of ions
Heat of Neutralisation
Formula: $q=mc\Delta T$
Question: Calculate the heat of neutralisation of a reaction.

Write balanced equation for reaction

Calculate number of moles of each reagent to find any limiting reagent

If there is limiting reagent, find the new mass that is full volume of limiting reagent + volume of other reagent that reacts (calculate using c=n/v, with n as the moles of limiting reagent)

Substitute values into equation
 c (for water) = 4.18
 m (in L if using 4.18, in mL if using 4.18 x 10^3) q in J/mol mass is the amount that is used to react (not the full volume/mass of reagents)
 q in J/mol
Enthalpy of Neutralisation
Formula: $H_n =\frac{q}{n}$
pH (Power of Hydrogen)
Formula: $pH=log_{10}[H^+]$
SelfIonisation Constant
Formula: $K_w=[\ce{OH}\times [\ce{H3O+}]$
Concentration of $\ce{H+}$ or $\ce{OH}$ ions (Strong Acids/Bases)
Formulae:
 $[\ce{H+}]=10^{pH}$
 $[\ce{OH}]=10^{pOH}$
 $[\ce{H+}]=\frac{10^{14}}{[\ce{OH}]}$
Question: Calculate the pH of a nonreacting solution (Dilution)
Procedure:

Calculate number of moles of acid/base

Calculate total volume of final solution

Calculate the new concentration in moles using combined volumes of mixtures (c = n/v)

If acid/base is strong, [H+] = [acid]

Calculate pH or pOH using formula
Question: Calculate the pH of a reacting solution (Neutralisation)
Procedure:

Write balanced chemical equation for reaction

Calculate number of moles for both reacting solutions

Use mole ratios to determine the excess reagent

Calculate the number of moles of the excess H or OH ions

Find the new concentration in using the combined volume of mixtures (c = n/v)

Calculate pH or pOH using formula
Heat of Combustion
Formula: $H_c =\frac{q}{n}$
Question: Calculate the mass of [substance] that must be burnt to increase the temperature of water by [amount].
Procedure:

Calculate the heat of neutralisation for water (q = mcat)

Sub value into the heat of combustion (h = q/n) to find number of moles

Use mole ratios to determine number of moles of ethanol required

Convert moles to mass (m = n x MM)
Percentage Yield
Formula: $\text{% Yield} = \frac{\text{Actual Mass}}{\text{Theoretical Mass}} \times 100\text{%}$
Percentage Purity
Formula: $\text{% Purity}=\frac{\text{Mass of useful product}}{\text{Total mass of sample}}\times 100$
Percentage Ionisation
Formula: $\text{% Ionisation}=\frac{[\ce{A}]}{[\ce{HA}]}\times 100\text{%}$