1--- 2header-includes: 3- \usepackage{mhchem} 4columns: 2 5geometry: margin=2cm 6--- 7 8# Rates and Equilibria 9 10## Energy profile diagrams 11 12$$E_A = E_{\text{max}} - E_{\text{initial}}$$ 13 14- Energy always needed to initiate reaction (break bonds of reactants) 15- Reactant particles must collide at correct angle, energy etc 16- Most collisions are not fruitful 17- Energy must be greater than or equal to $E_A$ 18 19**Endothermic** (products > reactants, $\Delta H > 0$) 20**Exothermic** (reactants > products, $\Delta H < 0$) 21 22 23 24 25**Ways to increase rate of reaction:** 26 271. Increase surface area 282. Increase concentration/pressure 293. Increase temperature 30 31## Kinetic energy 32 33**Temperature** - measure of _avg_ kinetic energy of particles. Over time each particle will eventually have enough energy to overcome $E_A$. 34Note same distribution indicates same temperature. 35 36 37## Catalysts 38 39- alternate reaction pathway, with lower $E_A$ 40- increased rate of reaction 41- involved in reaction but regenerated at end 42- does not alter $K_c$ or extent of reaction 43- attracts reaction products 44- removal/addition of catalyst does not push system out of equilibrium 45 46**Homogenous** catalyst: same state as reactants and products, e.g. Cl* radicals. 47**Hetrogenous** catalyst: different state, easily separated. Preferred for manufacturing. 48 49 50Many catalysts involve transition elements. 51Haber process (ammonia producition) - enzymes are catalysts for one reaction each. Adsorption (bonding on surface) forms ammonia \ce{NH3} 52 53## Equilibrium systems 54 55*Equilibrium* - the stage at which quantities of reactants and products remain unchanged 56 57Reaction graphs - exponential/logarithmic curves for reaction rates with time (simultaneous curves forward/back) 58 59{#id .class width=20%} 60**Complete reaction** - all reactant becomes product 61 62{#id .class width=20%} 63**Incomplete reaction** - goes both ways and reaches equilibrium 64 65- All reactions are equilibrium reactions, but extent of backwards reaction may be negligible 66- Double arrow indicates equilibrium reaction 67- At equilibrium, rate of forward reaction = rate of back reaction. 68 69### States (not in course) 70 71- **Homogeneous** - all states are the same 72- **Heterogeneous** - states are different 73 74## Equilibrium constant $K_c$ 75 76For \ce{$\alpha$A + $\beta$B + $\dots$ <=> $\chi$X + $\psi$Y + $\dots$}: 77 78$$K_c = {{[\ce{X}]^\chi \cdot [\ce{Y}]^\psi \cdot \dots} \over {[\ce{A}]^\alpha \cdot [\ce{B}]^\beta \cdot \dots}}$$ 79 80More generally, for reactants $n_i \ce{R}_i$ and products $m_i \ce{P}_i$: 81 82$$K_c = {{\prod\limits^{|P|}_{i=1} [P_i]^{m_i}} \over {\prod\limits^{|R|}_{i=1} [R_i]^{n_i}}} \> | \> i \in \mathbb{N}^*$$ 83 84Indicates extent of reaction 85If value is high ($> 10^4$), then [products] > [reactants] 86If value is low ($< 10^4$), then [reactants] > [products] 87 88- **$K_c$ depends on direction that equation is written (L to R)** 89- If $K_c$ is small, equilibrium lies *to the left* 90- aka *equilibrium expression* 91 92## Reaction constant (quotient) $Q$ 93 94Proportion of products/reactants at a give time (specific $K_C$). If $Q=K_c$, then reaction is at equilibrium. 95 96## Le Châtelier’s principle 97 98> 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. 99 100### Changing volume / pressure 101 1021. $\Delta V < 0 \implies [\Sigma \text{particles}] \uparrow$, therefore system reacts in direction that produces less particles 1032. $\Delta V > 0 \implies [\Sigma \text{particles}] \downarrow$, therefore system reacts in direction that produces more particles 1042. $n(\text{left}) = n(\text{right})$ (volume change does not disturb equilibrium) 105 106### Changing temperature 107 108Only method that alters $K_c$. 109 110Changing temperature changes kinetic energy. System's response depends on whether reaction is exothermic or endothermic. 111 112- Exothermic - increase temp decreases $K_c$ 113- Endothermic - increase temp increases $K_c$ 114 115Time-concentration graph: smooth change 116 117### Changing concentration 118 119- Decreasing "total" concentration of system causes a shift towards reaction which produces more particles 120 121## Yield 122 123$$\text{yield \%} = {{\text{actual mass obtained} \over \text{theoretical maximum mass}} \times 100}$$ 124 125## Acid/base equilibria 126 127Strong acid: $\ce{HA -> H+ + A-}$ 128Weak acid: $\ce{HA <=> H+ + A-}$ 129 130For weak acids, dilution causes increase in % ionisation. 131$\therefore [\ce{HA}] \propto 1 \div \text{\% ionisation}$ 132(see 2013 exam, m.c. q20) 133 134$$\text{\% ionisation} = {{[\ce{H+}] \over [\ce{HA}]} \times 100}$$ 135 136When a weak acid is diluted: 137 138- amount of $\ce{H3O+}$ increases 139- equilibrium shifts right 140- overall $[\ce{H3O+}]$ decreases 141- therefore pH increases