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# Calculation of ammonia thermodynamic properties

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1. In the table below is the thermodynamic data for ammonia (http://en.wikipedia.org/wiki/Ammonia_%28data_page%29) use this data to solve the following problems for mole of ammonia (state any assumptions you made):
a. What is the melting point at standard conditions for ammonia? Boling point is given -33.4C.
Assume you have a sample of liquid ammonia that is somehow at 0C but has not changed phase. Do not include in your calculation how it got to 0C.

b. What is the enthalpy change for boiling ammonia at 0C?
c. What is the entropy change for boiling ammonia at 0C?
d. What is the free energy change for boiling ammonia at 0C?
Property Value in J/mole or J/moleK
∆fus H 5.7X103
∆vap H 23.4 X 103
∆fus S 28.9
∆vap S 97.4
Cp (lq) 80.8
Cp(gas) 35.0
Note the standard heat capacity given is for 25C and you can solve the problem assuming it is constant between 0 and -33C. However if you go to the page referenced above you will see the heat capacity relationship with T could be better approximated in this range by a line.

Part 2 of question 1: Resolve the problem parts b-d using the following line (Cp=0.105T+78.68).
2. Derive the equation of state
3. Assume you have gas that follows the equation of state p[(V/n)-b]=RT (b is a constant for the gas and n is the number of moles of gas). Determine the equation for α the thermal expansion coefficient.

https://brainmass.com/physics/heat-thermodynamics/calculation-ammonia-thermodynamic-properties-618663

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Hello,
1. In the table below is the thermodynamic data for ammonia (http://en.wikipedia.org/wiki/Ammonia_%28data_page%29) use this data to solve the following problems for mole of ammonia (state any assumptions you made):
a. What is the melting point at standard conditions for ammonia? Boling point is given -33.4C.
Assume you have a sample of liquid ammonia that is somehow at 0C but has not changed phase. Do not include in your calculation how it got to 0C.

b. What is the enthalpy change for boiling ammonia at 0C?
c. What is the entropy change for boiling ammonia at 0C?
d. What is the free energy change for boiling ammonia at 0C?
Property Value in J/mole or J/moleK
∆fus H 5.7 x 103
∆vap H 23.4 x 103
∆fus S 28.9
∆vap S 97.4
Cp (lq) 80.8
Cp(gas) 35.0
Note the standard heat capacity given is for 25C and you can solve the problem assuming it is constant between 0 and -33C. However if you go to the page referenced above you will see the heat capacity relationship with T could be better approximated in this range by a line.

Part 2 of question 1: Resolve the problem parts b-d using the following line (Cp=0.105T+78.68).

Solution.

a)

Standard entropy of fusion is given as (see Ref. 1)

,
where is standard enthalpy of fusion and is melting point. Using data given in the table we can calculate melting point as

Part 1 - heat capacity is constant in given temperature range

b)

From definition of heat capacity (Ref. 2) (if we assume that enthalpy and heat capacity change with temperature) we have

or

.

We get now

. (*)
If we assume that heat capacity is constant we have now:

So, we have that boiling point is or and corresponding enthalpy . At or we will have that change of enthalpy, from previous equation, is ( ):

c)

The entropy change will be then (analogous to the equation in a))

d)

Gibbs free energy is know as

Part 2 - heat capacity is not a constant in given temperature range

b)

We have that heat capacity is the next function of temperature ,
Where and . Now equation (*) is (I put for simplicity )

Now it is easy to calculate

c)

d)

Gibbs free energy is know as

2. Derive the equation of state

Solution.

To derive this equation of state we will need one of the Maxwell relations (Ref. 3). So let's first derive this. We know that the differential form of internal energy is

(*)

and that Helmholtz Free energy is given as

(**)
Helmholtz Free energy is function , so total derivative is

If we compare this to the equation (**) we see that

and

If we do partial derivative of last two equations with respect to T (const. V) and V (const. T), respectively, we get

and

Left sides of last two equation are equal, so we get one of the Maxwell's relations

(***)

Ok, let go back to the our original problem, derivation of the equation of state. To do this, let's do derivative of internal energy (*) with respect to V (const. V)

we get next

If we now use our derived Maxwell relation (***) for , we get our equation of state:

3. Assume you have gas that follows the equation of state p[(V/n)-b]=RT (b is a constant for the gas and n is the number of moles of gas). Determine the equation for α the thermal expansion coefficient.

Solution.

Thermal expansion coefficient, , is defined (see Ref. 4.) as . We have equation of state:
.

Because we need to do partial derivative of with respect to the , when pressure is constant, we express our equation of state as:

We have now that partial derivative is:

Thermal expansion coefficient is then:

References

 https://en.wikipedia.org/wiki/Entropy#Phase_transitions

 https://en.wikipedia.org/wiki/Heat_capacity

 https://en.wikipedia.org/wiki/Maxwell_relations

[4 ]https://en.wikipedia.org/wiki/Thermal_expansion#Coefficient_of_thermal_expansion

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