chem / reactions.mdon commit [spec] start vector calculus (42fe40b)
   1---
   2header-includes:
   3  - \usepackage{mhchem}
   4  - \usepackage{tabularx}
   5columns: 2
   6geometry: margin=2cm
   7---
   8
   9# Rates and Equilibria
  10
  11## Energy
  12
  13### Enthalphy
  14
  15$$\Delta H = H_{\text{products}} - H_{\text{reactants}}$$
  16
  17**Endothermic** (products > reactants, $\Delta H > 0$)  
  18**Exothermic** (reactants > products, $\Delta H < 0$)
  19
  20![](graphics/endothermic-profile.png){#id .class width=25%}
  21![](graphics/exothermic-profile.png){#id .class width=25%}
  22
  23### Activation energy $E_A$
  24
  25$$E_A = E_{\text{max}} - E_{\text{initial}}$$
  26
  27- Energy always needed to initiate reaction (break bonds of reactants)
  28- Reactant particles must collide at correct angle, energy etc
  29- Most collisions are not fruitful
  30- Energy must be greater than or equal to $E_A$
  31
  32### Kinetic energy
  33
  34- **Temperature** - measure of _avg_ kinetic energy of particles. Over time each particle will eventually have enough energy to overcome $E_A$
  35- Note same distribution indicates same temperature
  36- $\uparrow$ rate with $\uparrow T$ mainly caused by $\uparrow E_K \implies$ greater collision force
  37![](graphics/ke-temperature.png)
  38
  39## Rates
  40
  41**Ways to increase rate of reaction:**
  42
  431. Increase surface area
  442. Increase concentration/pressure
  453. Increase temperature
  46
  47### Catalysts
  48
  49- alternate reaction pathway, with lower $E_A$
  50- increased rate of reaction
  51- involved in reaction but regenerated at end
  52- does not alter $K_c$ or extent of reaction
  53- attracts reaction products
  54- removal/addition of catalyst does not push system out of equilibrium
  55
  56**Homogenous** catalyst: same state as reactants and products, e.g. Cl* radicals.  
  57**Hetrogenous** catalyst: different state, easily separated. Preferred for manufacturing.
  58![](graphics/catalyst-graph.png)
  59
  60- Many catalysts involve transition elements
  61- **Solid catalysts** - particles around catalyst with high surface energy *adsorb* gas molecules, lowering $E_A$
  62- **Haber process** (ammonia producition) - enzymes are catalysts for one reaction each. Adsorption (bonding on surface) forms ammonia \ce{NH3}.
  63
  64## Equilibrium systems
  65
  66*Equilibrium* - the stage at which quantities of reactants and products remain unchanged
  67
  68Reaction graphs - exponential/logarithmic curves for reaction rates with time (simultaneous curves forward/back)
  69
  70\begin{tabularx}{\columnwidth}{ | l | X |}
  71  \hline
  72  \parbox[c]{2.2cm}{\includegraphics[width=2cm]{graphics/rxn-complete.png} } & \textbf{Complete reaction} - all reactant becomes product \\
  73  \hline
  74  \parbox[c]{2.2cm}{\includegraphics[width=2cm]{graphics/rxn-incomplete.png} } & \textbf{Incomplete reaction} - goes both ways and reaches equilibrium \\
  75  \hline
  76\end{tabularx}
  77
  78- All reactions are equilibrium reactions, but extent of backwards reaction may be negligible
  79- Double arrow indicates equilibrium reaction
  80- At equilibrium, rate of forward reaction = rate of back reaction.
  81- Approaching equilibrium, forward rate $>$ back rate
  82
  83### Equilibrium constant $K_c$
  84
  85For \ce{$\alpha$A + $\beta$B + $\dots$ <=> $\chi$X + $\psi$Y + $\dots$}:
  86
  87$$K_c = {{[\ce{X}]^\chi \cdot [\ce{Y}]^\psi \cdot \dots} \over {[\ce{A}]^\alpha \cdot [\ce{B}]^\beta \cdot \dots}}$$
  88
  89More generally, for reactants $n_i \ce{R}_i$ and products $m_i \ce{P}_i$:
  90
  91$$K_c = {{\prod\limits^{|P|}_{i=1} [P_i]^{m_i}} \over {\prod\limits^{|R|}_{i=1} [R_i]^{n_i}}} \> | \> i \in \mathbb{N}^*$$
  92
  93Indicates extent of reaction  
  94If value is high ($> 10^4$), then [products] > [reactants]  
  95If value is low ($< 10^4$), then [reactants] > [products]
  96
  97- **$K_c$ depends on direction that equation is written (L to R)**
  98- If $K_c$ is small, equilibrium lies *to the left*
  99- aka *equilibrium expression*
 100- For reverse reaction, use $K_c^\prime = {1 \over K_c}$
 101- For coefficients, use $K_c^\prime = K_c^n$
 102
 103## Reaction constant (quotient) $Q$
 104
 105Proportion of products/reactants at a give time (specific $K_C$). If $Q=K_c$, then reaction is at equilibrium.
 106
 107## Le Châtelier’s principle
 108
 109> 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.
 110
 111### Changing volume / pressure
 112
 1131. $\Delta V < 0 \implies [\Sigma \text{particles}] \uparrow$, therefore system reacts in direction that produces less particles
 1142. $\Delta V > 0 \implies [\Sigma \text{particles}] \downarrow$, therefore system reacts in direction that produces more particles
 1152. $n(\text{left}) = n(\text{right})$ (volume change does not disturb equilibrium)
 116
 117### Changing temperature
 118
 119Only method that alters $K_c$.
 120
 121Changing temperature changes kinetic energy. System's response depends on whether reaction is exothermic or endothermic.
 122
 123- Exothermic - increase temp decreases $K_c$
 124- Endothermic - increase temp increases $K_c$
 125
 126Time-concentration graph: smooth change
 127
 128### Changing concentration
 129
 130- Decreasing "total" concentration of system causes a shift towards reaction which produces more particles
 131
 132## Yield
 133
 134$$\text{yield \%} = {{\text{actual mass obtained} \over \text{theoretical maximum mass}} \times 100}$$
 135
 136- Yield may be lower than expected due to equilibrium reaction (incomplete)
 137- $\uparrow$ yield $\equiv$ forward rxn; $\downarrow$ yield $\equiv$ back rxn
 138- *Rate-yield conflict*: rxn is slower at eq. point further to RHS
 139- This is ameliorated by catalysts, high pressure and removal of product
 140
 141## Acid/base equilibria
 142
 143Strong acid: $\ce{HA -> H+ + A-}$  
 144Weak acid: $\ce{HA <=> H+ + A-}$
 145
 146For weak acids, dilution causes increase in % ionisation.  
 147$\therefore [\ce{HA}] \propto 1 \div \text{\% ionisation}$  
 148(see 2013 exam, m.c. q20)
 149
 150$$\text{\% ionisation} = {{[\ce{H+}] \over [\ce{HA}]} \times 100}$$
 151
 152When a weak acid is diluted:
 153
 154- amount of $\ce{H3O+}$ increases
 155- equilibrium shifts right
 156- overall $[\ce{H3O+}]$ decreases
 157- therefore pH increases