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{#id .class width=25%} 21{#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 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 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