Thermodynamics Thermodynamics is the study of systems involving energy in the form of heat and work.

First Law of Thermodynamics The change in internal energy of a system (  U) must be related to the energy exchange of heat (q) and work (w).  U = q + w  U, q and w are measured in joules (J) the metric unit for energy

First Law of Thermodynamics q is positive if heat is added to the system, and negative if heat is released. w is positive if work is done on the system, and negative if work is done by the system.

What does it mean for the system to do work? Work is simply a force multiplied by the distance moved in the direction of the force. A good example of a thermodynamic system that can do work is the gas confined by a piston in a cylinder.

An example of how work is done by a thermodynamic system  If the gas is heated, it will expand and push the piston up, doing negative work on the piston.  If the piston is pushed down, the piston does positive work on the gas.

 U = q –  VP Pressure-Volume Work Work = Force x distance For a chemical system the expansion or contraction of a gas is one type of work. So, Work (w) = -P  V *V f -V i will be negative when work is done on the system, but work done on the system must be positive thus the negative sign.

Sign Conventions Positive sign – energy is absorbed from the surroundings, and work is done on the system Negative sign - energy is released to the surroundings and work is done by the system.

Calorimetry Heat capacity- the quantity of heat needed to change the temperature of the system 1K C p = q/  T (units are J/k or J/ o c) Specific Heat capacity – the quantity of heat need to raise the temperature of 1 gram of a substance 1 o C q = C m  T

Specific Heat The quantity of heat required to raise 1 gram of water 1 o C. The higher the specific heat the harder it is to change the temperature of the substance.C (J/g o C) Al.092 Cu..385 Ethanol2.46 Water4.182

Calorimetry Measures the amount of heat generated from a chemical reaction by letting the heat generated flow into a mass of cooler water. q= m  T C q = heat  T = T f – T i m = mass C = specific heat (J/g o C)

Coffee Cup Calorimeter When a chemical reaction occurs in the coffee cup calorimeter, the heat of the reaction if absorbed by the water. The change in the water temperature is used to calculate the amount of heat that has been absorbed or evolved in the reaction.

For example, A chemical reaction occurs in 200 grams of water with an initial temperature of 25.0°C. As a result of the reaction, the temperature of the water changes to 31.0°C. The heat flow is calculated: q water = 4.18 J/(g·°C) x 200 g x (31.0°C °C) q water = +5.0 x 10 3 J ΔH reaction = -(q water )

Bomb Calorimeter A bomb calorimeter is used to measure heat flows for gases and high temperature reactions. In a bomb calorimeter, the reaction takes place in a sealed metal container, which is placed in the water in an insulated container.

Bomb Calorimeter Analysis of the heat flow is more complex than for the coffee cup calorimeter because the heat flow into the metal parts of the calorimeter must be accounted for (heat capacity, C p ): q reaction = - (q water + q bomb ) where q water = 4.18 J/(g·°C) x m water x Δt q bomb = C p x Δt

Calorimetry A g sample of glucose (C 6 H 12 O 6 ) was ignited in a bomb calorimeter. The temperature increased by o c. The heat capacity of the calorimeter was 3.56 kJ/ o c, and the calorimeter contained 1.00 kg of water. Find the molar heat in kJ/mol rxn C 6 H 12 O O 2  6 CO H 2 O

Calorimetry q bomb = kJ/ o c (3.682 o c) = kJ q water = 1000g (4.184 J/g o c) (3.682 o c) = J Q total = q bomb + q water q total = kJ (exothermic) per mol rxn g / g/mol = mol kJ/ mol = kJ/molrxn

Enthalpy Enthalpy is a measure of the total emery of a thermodynamic system. Most chemistry reactions take place at constant pressure, open to the atmosphere. So, Enthalpy (H) is used to describes these types of reactions. H = U + PV

Enthalpy (H) – The Heat of the Reaction The change in enthalpy (  H) is equal to the difference in the heat of the reaction.  H =  H final –  H initial =  H products –  H reactants Heat of formation (  H o f ) - the change in enthalpy when a compound forms from its pure elements. (table in back of text book)   H o f of a pure element = 0

Enthalpy and Internal Energy  H =  U +  VP  V P =  n gas const. T and P  H =  U +  n gas RT   U and  H are very close to the same value and are the same when no gas is generated by the reaction.

Hess’s Law The heat of a reaction is equal to the sum of the individual  H values for each step. Example: What is the  H for C + ½ O 2  CO? CO + ½ O 2  CO 2  H = kJ C + O 2  CO 2  H = kJ

What is the  H for C + ½ O 2  CO? CO 2  CO + ½ O 2  H = kJ C + O 2  CO 2  H = kJ C + ½ O 2  CO  H = kJ