[chem] acid/base equilibria and tidy section on K_c value

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diff --git a/chem/reactions.md b/chem/reactions.md
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--- a/chem/reactions.md
+++ b/chem/reactions.md
@@ -1,3 +1,10 @@
+---
+header-includes:
+  - \usepackage{mhchem}
+columns: 2
+geometry: margin=2cm
+---
+

 # Rates and Equilibria
 
 ## Energy profile diagrams
 # Rates and Equilibria
 
 ## Energy profile diagrams


@@ -7,6 +14,10 @@ $$E_A = E_{\text{max}} - E_{\text{initial}}$$
 - 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 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, $\Delta H < 0$)

 
 ![](graphics/endothermic-profile.png)
 ![](graphics/exothermic-profile.png)
 
 ![](graphics/endothermic-profile.png)
 ![](graphics/exothermic-profile.png)


@@ -19,7 +30,7 @@ $$E_A = E_{\text{max}} - E_{\text{initial}}$$
 
 ## Kinetic energy
 
 
 ## 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.  
 ![](graphics/ke-temperature.png)
 
 Note same distribution indicates same temperature.  
 ![](graphics/ke-temperature.png)
 


@@ -28,6 +39,9 @@ Note same distribution indicates same temperature.
 - alternate reaction pathway, with lower $E_A$
 - increased rate of reaction
 - involved in reaction but regenerated at end
 - 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.
 
 **Homogenous** catalyst: same state as reactants and products, e.g. Cl* radicals.  
 **Hetrogenous** catalyst: different state, easily separated. Preferred for manufacturing.


@@ -38,33 +52,55 @@ Haber process (ammonia producition) - enzymes are catalysts for one reaction eac
 
 ## Equilibrium systems
 
 
 ## 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)
 
 Reaction graphs - exponential/logarithmic curves for reaction rates with time (simultaneous curves forward/back)
 

-## Equilirbium constant $K_C$
+![](graphics/rxn-complete.png){#id .class width=20%}
+**Complete reaction** - all reactant becomes product  
+
+![](graphics/rxn-incomplete.png){#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.
 
 
 ## 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
 2. $n(\text{left}) = n(\text{right})$ (volume change does not disturb equilibrium)
 
 ### Changing temperature


@@ -73,14 +109,33 @@ Only method that alters $K_c$.
 
 Changing temperature changes kinetic energy. System's response depends on whether reaction is exothermic or endothermic.
 
 
 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
 
 
 Time-concentration graph: smooth change
 

+### Changing concentration
+
+- Decreasing "total" concentration of system causes a shift towards reaction which produces more particles
+

 ## Yield
 
 ## 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

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