---
header-includes:
- \usepackage{mhchem}
+ - \usepackage{tabularx}
columns: 2
geometry: margin=2cm
---
# Rates and Equilibria
-## Energy profile diagrams
+## Energy
+
+### Enthalphy
+
+$$\Delta H = H_{\text{products}} - H_{\text{reactants}}$$
+
+**Endothermic** (products > reactants, $\Delta H > 0$)
+**Exothermic** (reactants > products, $\Delta H < 0$)
+
+{#id .class width=25%}
+{#id .class width=25%}
+
+### Activation energy $E_A$
$$E_A = E_{\text{max}} - E_{\text{initial}}$$
- 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 $E_A$
+- Note same distribution indicates same temperature
+- $\uparrow$ rate with $\uparrow T$ mainly caused by $\uparrow E_K \implies$ greater collision force
+
+
+## Rates
**Ways to increase rate of reaction:**
2. Increase concentration/pressure
3. Increase temperature
-## Kinetic energy
-
-**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.
-
-
-## Catalysts
+### Catalysts
- alternate reaction pathway, with lower $E_A$
- increased rate of reaction
**Hetrogenous** catalyst: different state, easily separated. Preferred for manufacturing.
-Many catalysts involve transition elements.
-Haber process (ammonia producition) - enzymes are catalysts for one reaction each. Adsorption (bonding on surface) forms ammonia \ce{NH3}
+- Many catalysts involve transition elements
+- **Solid catalysts** - particles around catalyst with high surface energy *adsorb* gas molecules, lowering $E_A$
+- **Haber process** (ammonia producition) - enzymes are catalysts for one reaction each. Adsorption (bonding on surface) forms ammonia \ce{NH3}.
## Equilibrium systems
Reaction graphs - exponential/logarithmic curves for reaction rates with time (simultaneous curves forward/back)
-{#id .class width=20%}
-**Complete reaction** - all reactant becomes product
-
-{#id .class width=20%}
-**Incomplete reaction** - goes both ways and reaches equilibrium
+\begin{tabularx}{\columnwidth}{ | l | X |}
+ \hline
+ \parbox[c]{2.2cm}{\includegraphics[width=2cm]{graphics/rxn-complete.png} } & \textbf{Complete reaction} - all reactant becomes product \\
+ \hline
+ \parbox[c]{2.2cm}{\includegraphics[width=2cm]{graphics/rxn-incomplete.png} } & \textbf{Incomplete reaction} - goes both ways and reaches equilibrium \\
+ \hline
+\end{tabularx}
- 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.
+- Approaching equilibrium, forward rate $>$ back rate
-### States (not in course)
-
-- **Homogeneous** - all states are the same
-- **Heterogeneous** - states are different
-
-## Equilibrium constant $K_c$
+### Equilibrium constant $K_c$
For \ce{$\alpha$A + $\beta$B + $\dots$ <=> $\chi$X + $\psi$Y + $\dots$}:
- **$K_c$ depends on direction that equation is written (L to R)**
- If $K_c$ is small, equilibrium lies *to the left*
- aka *equilibrium expression*
+- For reverse reaction, use $K_c^\prime = {1 \over K_c}$
+- For coefficients, use $K_c^\prime = K_c^n$
## Reaction constant (quotient) $Q$
$$\text{yield \%} = {{\text{actual mass obtained} \over \text{theoretical maximum mass}} \times 100}$$
+- Yield may be lower than expected due to equilibrium reaction (incomplete)
+- $\uparrow$ yield $\equiv$ forward rxn; $\downarrow$ yield $\equiv$ back rxn
+- *Rate-yield conflict*: rxn is slower at eq. point further to RHS
+- This is ameliorated by catalysts, high pressure and removal of product
+
## Acid/base equilibria
Strong acid: $\ce{HA -> H+ + A-}$