+---
+header-includes:
+ - \usepackage{mhchem}
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+
# Rates and Equilibria
## Energy profile diagrams
- Energy always needed to initiate reaction (break bonds of reactants)
- Reactant particles must collide at correct angle, energy etc
- Most collisions are not fruitful
+- Energy must be greater than or equal to $E_A$
+
+**Endothermic** (products > reactants, $\Delta H > 0$)
+**Exothermic** (reactants > products, $\Delta H < 0$)
## Kinetic energy
-Temperature - measure of _avg_ kinetic energy of particles. Over time each particle will eventually have enough energy to overcome $E_A$.
+**Temperature** - measure of _avg_ kinetic energy of particles. Over time each particle will eventually have enough energy to overcome $E_A$.
Note same distribution indicates same temperature.
- alternate reaction pathway, with lower $E_A$
- increased rate of reaction
- involved in reaction but regenerated at end
+- does not alter $K_c$ or extent of reaction
+- attracts reaction products
+- removal/addition of catalyst does not push system out of equilibrium
**Homogenous** catalyst: same state as reactants and products, e.g. Cl* radicals.
**Hetrogenous** catalyst: different state, easily separated. Preferred for manufacturing.
## Equilibrium systems
-**Equilibrium** - the stage at which quantities of reactants and products remain unchanged
+*Equilibrium* - the stage at which quantities of reactants and products remain unchanged
+
Reaction graphs - exponential/logarithmic curves for reaction rates with time (simultaneous curves forward/back)
-## Equilirbium constant $K_C$
+{#id .class width=20%}
+**Complete reaction** - all reactant becomes product
+
+{#id .class width=20%}
+**Incomplete reaction** - goes both ways and reaches equilibrium
+
+- All reactions are equilibrium reactions, but extent of backwards reaction may be negligible
+- Double arrow indicates equilibrium reaction
+- At equilibrium, rate of forward reaction = rate of back reaction.
+
+### States (not in course)
+
+- **Homogeneous** - all states are the same
+- **Heterogeneous** - states are different
-For reaction $aA + bB + cC + dD + \dots \leftrightarrow zZ + yY + xX + \dots$:
+## Equilibrium constant $K_c$
-$$K_c = {{[Z]^z [Y]^y [X]^x \dots} \over {[A]^a [B]^b [C]^c [D]^d \dots}}$$
+For \ce{$\alpha$A + $\beta$B + $\dots$ <=> $\chi$X + $\psi$Y + $\dots$}:
-Indicates extent of reaction. If value is high ($> 10^4$), then [products] > [reactants]. If value is low ($< 10^4$), then [reactants] > [products].
+$$K_c = {{[\ce{X}]^\chi \cdot [\ce{Y}]^\psi \cdot \dots} \over {[\ce{A}]^\alpha \cdot [\ce{B}]^\beta \cdot \dots}}$$
-If $K_c$ is small, equilibrium lies *to the left*.
+More generally, for reactants $n_i \ce{R}_i$ and products $m_i \ce{P}_i$:
-**$K_c$ depends on direction that equation is written (L->R)**
+$$K_c = {{\prod\limits^{|P|}_{i=1} [P_i]^{m_i}} \over {\prod\limits^{|R|}_{i=1} [R_i]^{n_i}}} \> | \> i \in \mathbb{N}^*$$
-## Reaction constant $Q$
+Indicates extent of reaction
+If value is high ($> 10^4$), then [products] > [reactants]
+If value is low ($< 10^4$), then [reactants] > [products]
-Same for as $K_C$. If $Q=K_c$, then reaction is at equilibrium.
+- **$K_c$ depends on direction that equation is written (L to R)**
+- If $K_c$ is small, equilibrium lies *to the left*
+- aka *equilibrium expression*
+
+## Reaction constant (quotient) $Q$
+
+Proportion of products/reactants at a give time (specific $K_C$). If $Q=K_c$, then reaction is at equilibrium.
## Le Châtelier’s principle
> Any change that affects the position of an equilibrium causes that equilibrium to shift, if possible, in such a way as to partially oppose the effect of that change.
-### Changing volume
+### Changing volume / pressure
-1. $\Delta V \implies [\Sigma \text{particles}] \uparrow$, therefore system reacts in direction that produces less particles
-2. $\Delta V \implies [\Sigma \text{particles}] \uparrow$, therefore system reacts in direction that produces more particles
+1. $\Delta V < 0 \implies [\Sigma \text{particles}] \uparrow$, therefore system reacts in direction that produces less particles
+2. $\Delta V > 0 \implies [\Sigma \text{particles}] \downarrow$, therefore system reacts in direction that produces more particles
2. $n(\text{left}) = n(\text{right})$ (volume change does not disturb equilibrium)
### Changing temperature
Changing temperature changes kinetic energy. System's response depends on whether reaction is exothermic or endothermic.
-- Exothermic - increase in temperature decreases $K_c$
-- Endothermic - increase in temperature increases $K_c$
+- Exothermic - increase temp decreases $K_c$
+- Endothermic - increase temp increases $K_c$
Time-concentration graph: smooth change
+### Changing concentration
+
+- Decreasing "total" concentration of system causes a shift towards reaction which produces more particles
+
## Yield
-$$\text{yield %} = {{text{actual mass obtained} \over {theoretical maximum mass}} \times 100$$
+$$\text{yield \%} = {{\text{actual mass obtained} \over \text{theoretical maximum mass}} \times 100}$$
+
+## Acid/base equilibria
+
+Strong acid: $\ce{HA -> H+ + A-}$
+Weak acid: $\ce{HA <=> H+ + A-}$
+
+For weak acids, dilution causes increase in % ionisation.
+$\therefore [\ce{HA}] \propto 1 \div \text{\% ionisation}$
+(see 2013 exam, m.c. q20)
+$$\text{\% ionisation} = {{[\ce{H+}] \over [\ce{HA}]} \times 100}$$
+When a weak acid is diluted:
+- amount of $\ce{H3O+}$ increases
+- equilibrium shifts right
+- overall $[\ce{H3O+}]$ decreases
+- therefore pH increases