[chem] clarify yield, enthalpy and rates notes

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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
@@ -1,13 +1,26 @@
 ---
 header-includes:
   - \usepackage{mhchem}
 ---
 header-includes:
   - \usepackage{mhchem}

+  - \usepackage{tabularx}

 columns: 2
 geometry: margin=2cm
 ---
 
 # Rates and Equilibria
 
 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, $\Delta H < 0$)
+
+![](graphics/endothermic-profile.png){#id .class width=25%}
+![](graphics/exothermic-profile.png){#id .class width=25%}
+
+### Activation energy $E_A$

 
 $$E_A = E_{\text{max}} - E_{\text{initial}}$$
 
 
 $$E_A = E_{\text{max}} - E_{\text{initial}}$$
 


@@ -16,11 +29,14 @@ $$E_A = E_{\text{max}} - E_{\text{initial}}$$
 - Most collisions are not fruitful
 - Energy must be greater than or equal to $E_A$
 
 - 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

 
 

-![](graphics/endothermic-profile.png)
-![](graphics/exothermic-profile.png)
+- **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
+![](graphics/ke-temperature.png)
+
+## Rates

 
 **Ways to increase rate of reaction:**
 
 
 **Ways to increase rate of reaction:**
 


@@ -28,13 +44,7 @@ $$E_A = E_{\text{max}} - E_{\text{initial}}$$
 2. Increase concentration/pressure
 3. Increase temperature
 
 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.  
-![](graphics/ke-temperature.png)
-
-## Catalysts
+### Catalysts

 
 - alternate reaction pathway, with lower $E_A$
 - increased rate of reaction
 
 - alternate reaction pathway, with lower $E_A$
 - increased rate of reaction


@@ -47,8 +57,9 @@ Note same distribution indicates same temperature.
 **Hetrogenous** catalyst: different state, easily separated. Preferred for manufacturing.
 ![](graphics/catalyst-graph.png)
 
 **Hetrogenous** catalyst: different state, easily separated. Preferred for manufacturing.
 ![](graphics/catalyst-graph.png)
 

-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
 
 
 ## Equilibrium systems
 


@@ -56,22 +67,20 @@ Haber process (ammonia producition) - enzymes are catalysts for one reaction eac
 
 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)
 

-![](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  
+\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.
 
 - 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 + $\dots$}:
 
 
 For \ce{$\alpha$A + $\beta$B + $\dots$ <=> $\chi$X + $\psi$Y + $\dots$}:
 


@@ -88,6 +97,8 @@ If value is low ($< 10^4$), then [reactants] > [products]
 - **$K_c$ depends on direction that equation is written (L to R)**
 - If $K_c$ is small, equilibrium lies *to the left*
 - aka *equilibrium expression*
 - **$K_c$ 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) $Q$
 
 
 ## Reaction constant (quotient) $Q$
 


@@ -122,6 +133,11 @@ Time-concentration graph: smooth change
 
 $$\text{yield \%} = {{\text{actual mass obtained} \over \text{theoretical maximum mass}} \times 100}$$
 
 
 $$\text{yield \%} = {{\text{actual mass obtained} \over \text{theoretical maximum mass}} \times 100}$$
 

+- 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: $\ce{HA -> H+ + A-}$  
 ## Acid/base equilibria
 
 Strong acid: $\ce{HA -> H+ + A-}$  

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