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LECTURE 5

Page history last edited by Khoa Tran 14 years, 5 months ago

Dr. Cooper's comments:

 

 

Obed Tawiah-Ampah (burgundy)

[C] The variation of enthalpy with temperature 

 

The enthalpy of a system can be quantified by its relationship to the amount of heat it can absorb at a constant volume or, it’s Heat Capacity at Constant Pressure (Cp). Since the amount of a substance in our system is not required, we consider Cp an extensive property.


 

Eqn .1  Formula

Enthalpy change (dH) is the amount of heat (q) supplied to or from a system. Since heat transferred is expressed in terms of enthalpy change the two are interchangeable (dH =dq) at constant pressure. Now you must be asking, how does this help us when we are speaking in constant volume terms?

Because in a constant pressure system we can only do expansion and no compression work so our change in enthalpy is equal to our amount of heat.

So Formula  can be viewed as

 

Eqn.2    Formula

Where under constant pressure, the change in enthalpy is dependent on the change in temperature.


Now, should the molar quantities of a system come into play (a < b) there is a variation of the heat capacity equation that allows for highly accurate results. Equation 3 is based on a per mole basis. We know that any value based on the amount of that substance is an intensive property.

Eqn.3     Formula

To help understand this note the data table 2.2

 

**Note the difference in the molar heat capacities of solid Carbon and gaseous Carbon dioxide. Their molar values show decreasingly less variation as temperatures increase.

 

The system does its best to dump heat back into the surroundings, so the temperature rises slowly even though it takes on heat.  That is the beauty of specific heat. The greater the specific heat of a system, the more energy required to raise the temperature.

As you can imagine, we can use the heat capacities interchangeably.

Eqn 4.    Formula

Because we look at many of these properties under a vast number of changes we can express the enthalpy change as an integral over the bound of the change in temperature (dT)

Mike Toulouse (Black)

 

Adiabatic Changes

 

An adiabatic change is a change in which no heat is transferred from the system to the surroundings and vice versa.

 

The change in internal energy of an ideal gas when it expands adiabatically is,

 

                                                                                                        ∆U = CvTf- CiTi

                                                                                                        ∆U = Cv∆T                     Eqn 1

 

Since this equation deals with an ideal gas, the internal energy is independent of the volume.      

 

                                                                        ∆U = q + w                    Eqn 2

 

Also this is an adiabatic change so we know that q must be equal to 0.  By combining equations 1 and 2 you get,

 

 

                                                                                                       wad Cv∆T                      Eqn 3

 

                                           

What equation 3 tells us is that work done on an ideal gas in an adiabatic system is proportional to the initial and final temperature.  Using the equation from Further Information 2.1 it is shown that,

 

                                                                                                       Tf = Ti(Vi/Vf)1/c           where c = Cv,m/R

 

Adiabatic expansion can also be related to pressure using the following equation, if you sub pf and pi for Tf and Ti respectively, and if you sub c for ϒ, where ϒ= Cp,m/Cv,m.  

 

Adiabats occur when you plot pressure vs. volume for an adiabatic change.

 

Thermochemistry

 

Thermochemistry is the study of heat transfer during chemical reactions.

Each reaction can be used to find q because during the reaction there will either be a change in internal energy or a change in enthalpy.

There are two types of processes in thermochemistry, exothermic and endothermic.  Exothermic processes release energy by heating the surroundings (with pressure constant ∆H<0)

Endothermic processes absorb energy by cooling the surroundings (with pressure constant ∆H>0) 

 

Khoa Tran  (blue)

 

 

2.7

(a) Enthalpies of physical change

 

 

The standard enthalpy of transition: is the change in physical state of the standard enthalpy change.

For example, the standard enthalpy of vaporization, ∆vap H0, or the standard enthalpy of fusion, ∆fus H0.

 

 

Vaporization – the change from the state of liquid into gas.

Fusion – the change from the state of solid into liquid.

Sublimation – the change from the state of solid into gas.

 

 

The change in enthalpy is the dependent on the two states, the final and initial states.

 

Instead of arrows... I see a mailbox and a roll of film symbols??? 

H2O(s) -->    H2O(g)                 ∆sub H0

H2O(s) --> H2O(l)                  ∆fus H0

H2O(l) --> H2O(g)                 ∆vap H0

H2O(s) --> H2O(g)                 ∆fus H0  +  ∆vap H0

 

 

Overall, the state of solid to liquid = fusion, the state of liquid to gas = vaporization, the state of solid to gas = sublimation, therefore a conclusion can be the state of sublimation = fusion + vaporization.

 

 

The reverse of the standard enthalpy changes in the forward direction is in the opposite sign.

∆H0 ( A-->B) = -∆H0 ( B-->A) arrows again?

The above statement is clearly shown as the enthalpy of vaporization of water is 44 kJ mol-1 at 298 K, the enthalpy of condensation at that temperature is -44kJ mol-1.

 

 

(b) Enthalpies of chemical change

 

 

There are two method of reporting the enthalpy of chemical change: thermochemical equation and the standard reaction enthalpy.

 

 

The thermochemical equation is one of the methods to write a combination of chemical reaction with the corresponding changes.

 

arrow 

CH4(g) + 2O2(g) --> CO2(g) + 2H2O(l)             ∆H0 =-890kJ

 

 

∆H0 represents the change in enthalpy in the reaction from standard state of reactant to the standard state of product. However, there is an exception on the ionic reactions in solution, the enthalpy changes are consisted of mixing and separation are significant for comparison.

 

 

The second method of reporting the enthalpy change in chemical reaction is the standard reaction enthalpy, ∆rH0 , and it is mostly used for the combustion of reaction.

 

arrow 

CH4(g) + 2O2(g) --> CO2(g) + 2H2O(l)             ∆H0 =-890kJ mol-1

 

arrow 

The standard reaction enthalpy of the reaction 2 A + B --> 3 C + D would be:

rH0 = {3 H0 m(C) + H0 m(D)} – {2 H0 m(A) + H0 m(B)}

H0 m in this case is the standard molar enthalpy at a specific temperature.

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