Unit 1 - Energy

Thermochemistry: Energy and Energy Transfer

The study of energy changes that accompany physical and chemical changes

• Temperature vs Heat (q)
  • Temperature is avg kinetic energy of particles. Relates to How Entities Move. ONLY relates to speed
  • Heat: the overall thermal energy in a sample. $mass\ast speed$
    • Depends on:
    • Temperature * number of particles (mass) * type of solid particles (s/l/g)
• Systems
  • Anything that’s not in the system is a surrounding
  • Open: both energy and matter can be exchanged with surroundings (my room)
  • Closed: Only energy (sealed metal drum)
  • Isolated: neither energy nor matter (e.g. ISS/Thermus)
• Exothermic vs Endothermic
  • Exo: Gives off heat (hot pack)
  • Edo: Absorbs heat (cold pack)
• When you touch something, you feel thermal conductivity of the substance not simply it’s temperature.

Specific Heat Capacity

the heat required to raise the temperature of the unit mass of a given substance by a given amount (usually one degree)

Measuring Energy changes

$$\begin{array}{rl}& q_{\text{joule}}=mc\Delta T\\ & T_{final}=T_{initial}-\frac{q}{mc}\end{array}$$

where:

• $q$ is the energy in J or $kJ$
• $m$ is the mass in g or $kg$
• $c$ is the specific heat capacity in $J/g°C$ or $kJ/kg°C$
• $\Delta T$ is the change in temperature ($T_2-T_1$) in $°C$

Calorimeter

Isolated system. Food is burned to calculate calories

Bomb Calorimeter

(used to calculate higher energy items)

Energy Transfer

Energy is always transferred from an object of higher temperature to an object of a lower temperature until they are equal

Methods

• Conduction - transfer through direct touch
• Convection - transfer through fluids
• Radiation - transfer through space (no direct contact)

Calculations

$$\begin{array}{rl}& q_{gained}+q_{lost}=0\\ & q_{gained}=-q_{lost}\end{array}$$

The First Law of Thermodynamics

The total energy in the universe is constant therefore, the change in energy of the universe is $zero$

$$\begin{array}{r}{E}_{universe}=E_{system}+E_{surroundings}\\ \Delta E_{system}=-\Delta E_{surroundings}\end{array}$$

Phases

Calculating Energy Across Phase Changes

1. Break the process into segments: heating, phase changes, and cooling.
2. For temperature changes, use $q=mc\Delta T$ (specific heat), where $q$ is in joules. Convert to kJ by dividing by $1000$.
3. For phase changes, use $q=\text{moles}\cdot L$, where $L$ is the lat ent heat (fusion or vaporization) in kJ/mol.
4. Combine all contributions:
   $q_{\text{total}}=\sum \left(\frac{mc\Delta T}{1000}\right)+\sum \left(\text{moles}\cdot L\right)$
5. Ensure consistent units (mass in grams, $c$ in J/g°C, $\Delta T$ in °C, $L$ in kJ/mol).

Latent heat

$q_{\text{phase change}}=n\cdot L$

Enthalpy

H, is the heat content of the system

$$\begin{array}{rl}& Heat=energy+Pressure\times volume\\ & H=E+PV\end{array}$$

You can’t calculate the total enthalpy of a system but we can measure the change, $\Delta H$

$$\begin{array}{r}\Delta H=\Delta E+\Delta PV\end{array}$$

if $\Delta PV$ is zero, then

$$\Delta H=\Delta E=q$$

Enthalpy is the amount of heat produced during a change in state or chemical reaction. It’s represented in $\Delta H$ and generally has the unit of $kJ/mol$

$\Delta H$ is also equal to the difference in enthalpies in products and reactants

Types of enthalpies

Represented by subscript
2. Enthalpy of fusion $(\Delta H_{fus})$ - melting/freezing phase change
3. Enthalpy of vaporisation $(\Delta H_{vap})$- evaporation/condensation phase change
4. Enthalpy of reaction - $(\Delta H_r)$ energy change involved in a reaction
5. Enthalpy of combustion $(\Delta H_c)$ - energy released when $1mol$ of fuel undergoes combustion
6. Enthalpy of formation $(\Delta H_f)$ - energy required to produce $1mol$ of a chemical from it’s elements

Thermochemical equation

A chemical reaction + energy
e.g.

$$2H_{2(g)}+O_{2(g)}\to 2H_2{O}_{(l)}+590kJ$$

If the $\Delta H$ is negative (exothermic), then the energy is on the products side, if positive (endothermic) it would be on the reactants side.

Standard Molar Enthalpy, $\Delta H^{\circ }$

The same reaction carried out in different physical states can have Different $\Delta H$
i.e. change in state has an effect on the enthalpy. This is due to some energy required to do phase changes

even different temps/pressures can effect the enthalpy of action,

This is due to the fact that temp/pressure effect the state of a substance.

• We usually use $SATP$ for this reason
  • And when we use $SATP$, we represent $\Delta H$ as $\Delta H^{\circ }$

Calculating $\Delta H$

7. Using value of $q$ and the number of moles
   1. Used experimentally
8. Using Hess’ Law
9. Using Bond energies
10. Using Standard heats of formation (at $SATP$)
11. Potential energy diagrams

When $\Delta H$ is positive, it’s an exothermic reaction. If it’s negative, it’s an endothermic reaction.

If we are calculating q for the surroundings, then we would switch to $-q/n$ from $q/n$

Hess’s Law - Finding Enthalpy and heats of formation

$\Delta H$ of a reaction can be calculated algebraically using various reactions with known enthalpies

• equations can be reversed; the $|\Delta H|$ stays the same but the sign changes

Heats of formations

$$\sum (\Delta H_f\text{products})-\sum (\Delta H_f\text{reactants})$$ $$f\left(x\right)=\frac{2}{x}{\left(\frac{2}{10}x\right)}^2$$

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