Chemistry Equations
List of Equations and their uses for Preliminary and HSC Chemistry
Table of Contents
Gibbs Free Energy
Formula: $\Delta G=\Delta H-T\Delta S$
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) Table1 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 compound2
-
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: $pH=-log_{10}[H^+]$
Self-Ionisation 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 non-reacting 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: $\text{% Ionisation}=\frac{[\ce{A-}]}{[\ce{HA}]}\times 100\text{%}$