Lecture 7

Readings

http://umdberg.pbworks.com/w/page/50493326/Gibbs%20free%20energy

http://umdberg.pbworks.com/w/page/104491345/Example%3A%20Free%20energy%20of%20an%20expanding%20gas

Gibb's Free Energy

• Sign tells if the change can happen spontaneously

  • Negative = spontaneous
  • Positive = non-spontaneous

• Magnitude is the amount of energy "available" to do other work

• For a system:

  • $\mathrm{\Delta }G=\mathrm{\Delta }H-(T\ast \mathrm{\Delta }S)$$\Delta G = \Delta H - \left(T * \Delta S\right)$

  • $\mathrm{\Delta }H$$\Delta H$ is the change in enthalpy

    • Energy, Joules, Bond Energy, Expansion Energy, Volume Change

  • $\mathrm{\Delta }S$$\Delta S$ is the change in entropy

    • Not an energy
    • Units = $J/K$$J/K$

  • Works for constant pressure and temperature

   

• Example, $2\mathrm{H}⟶\mathrm{H}{\phantom{X}}_2$$\ce{2H ->H2}$

  

  • Worked out the enthalpy before
  • Define the system - just the $H$$H$ molecules
  • System can interact with the rest of the universe, (it's not isolated), so the system can pass heat energy to and from the universe
  • Enthalpy:
  $$\mathrm{\Delta }H=\frac{-435kJ}{1mole}-\frac{2.5kJ}{1mole}=\frac{-437.5kJ}{1mole}$$

   

  • Reminder: the $-435$$-435$ term is from forming bonds, the $-2.5$$-2.5$ term is from $P\ast \mathrm{\Delta }V$$P * \Delta V$ ( air pressure pushing on H gas system as number of molecules decrease )

  • So $\mathrm{\Delta }H$$\Delta H$ is negative

  • What is $\mathrm{\Delta }S$$\Delta S$ ?

    • Exact number is difficult, but probably negative since less molecules in a smaller volume

  • Note: Since $\mathrm{\Delta }S$$\Delta S$ for the system ( H molecules ) is negative, the $\mathrm{\Delta }S$$\Delta S$ for the rest of the universe must be increaseing

    • Net entropy for the entire universe can never decrease

  • So $-T\ast \mathrm{\Delta }S$$-T *\Delta S$ term will be positive

  • $\mathrm{\Delta }G=\mathrm{\Delta }H-(T\ast \mathrm{\Delta }S)$$\Delta G = \Delta H - \left(T * \Delta S\right)$

    • $\mathrm{\Delta }H$$\Delta H$ is negative, so it favors the reaction being spontaneous
    • $-T\ast \mathrm{\Delta }S$$-T * \Delta S$ is positive , so doesn't favor the reaction

  • So does the reaction occur spontaneously or not?

    • It depends

    • If $T$$T$ is low , then $\mathrm{\Delta }G$$\Delta G$ is probabily negative ( 1st term dominates )

    • if $T$$T$ is high enough , then $\mathrm{\Delta }G$$\Delta G$ will become positive ( 2nd term dominates ) and the reaction won't occur spontaneously

    • At low temperatures, the forming of bonds is favored, $\mathrm{H}+\mathrm{H}⟶\mathrm{H}{\phantom{X}}_2$$\ce{H + H -> H_2}$

    • At high temperatures, the thermal energy is high, molecules move faster, collisions are more violent, and bonds are likely to be broken

      • So $\mathrm{H}{\phantom{X}}_2⟶\mathrm{H}+\mathrm{H}$$\ce{H2 -> H + H}$

  

  

• Like boiling water

  • At room temperature, steam condenses to form liquid $H_{2}O$$H_2O$
  • Heat it enough and liquid $\mathrm{H}{\phantom{X}}_2\mathrm{O}⟶\mathrm{Steam}$$\ce{H2O -> Steam}$

• Bonding is favored based on 1st law of thermodynamics, but sometimes entropy ( 2nd law ) doesn't allow it