CH321 Thermodynamics: Hydrogen Peroxide Decomposition Analysis

This assignment solution addresses a thermodynamics homework problem focused on hydrogen peroxide (H2O2). The solution begins by examining the formation and stability of H2O2, predicting its spontaneity and shelf-life. It then delves into the decomposition reaction of H2O2, calculating Gibbs free energy (Grxn) at different temperatures and pressures, and discussing the implications for the reaction's spontaneity and the compound's shelf-life. The solution also explores the relationship between entropy, pressure, and temperature, deriving an equation for an ideal gas. Finally, the assignment analyzes a phase diagram for carbon, identifying triple points, normal fusion points, and describing phase changes under varying conditions of temperature and pressure, including the conditions necessary to convert graphite to diamond.

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Thermodynamics
Name
Institutional Affiliation

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CH321 Exam 2
1. For this problem, consider the case of hydrogen peroxide.
a. Write down the formation reaction for H2O2 (liq). Is the compound stable with respect to
its elements at SATP? What can you predict about the spontaneity of the reaction and the
shelf-life of H2O2 (liq) from this data alone?
H2 ( g ) +O2 ( g ) → H2 O2 (l )
Compound formed isunstable .readily breaks down ¿ water∧single
oxygen molecule .
Hydrogen peroxide is a strong oxidizing agent it decomposes it can cause
spontaneous combustion when it comes in contact with organic material. Due to
its instability nature, the compound has a short shelf life.
Now consider the decomposition reaction of pure hydrogen peroxide:
H2O2 (liq) →H2O (liq) + ½ O2 (g)
Using the data given below and assuming that the ideal gas law applies to the gas.
Density at SATP:
H2O2 (liq) = 1.45g/mL BP: H2O2 (liq) = 423 K
H2O (liq) = 0.997g/mL BP: H2O (liq) = 373 K

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Possibly useful conversion: 10 mL×bar = 1 J
b. Find ∆Grxn for the decomposition reaction at 298K and exactly 1 bar pressure. Is the
reaction spontaneous under these conditions? What can you now predict about the shelf-
life of H2O2 (liq) from the data given?
∆ Greaction=∆ H−T ∆ S
H2O2 (liq) →H2O (liq) + ½ O2 (g)
∆ H =−187.78
∆ S= ( 1 x 69.91 ) + 1
2 x ¿) =172.6Kj/mol
T =298 k
∆ Greaction=−187.78−(298 x 172.6
1000 )
∆ Greaction=−187.78−51434.8
1000
¿−239.21 kJ / mol
The reaction is spontaneous and shelf life is too short.
c. Find∆Grxn for the decomposition reaction at 350K and 1 bar (you may assume that ∆
Grxn and the heat capacities are all independent of temperature over this temperature
range).
∆ Greaction=∆ H−T ∆ S
H2O2 (liq) →H2O (liq) + ½ O2 (g)
∆ H =−187.78
∆ S= ( 1 x 69.91 ) + 1
2 x ¿) =172.6Kj/mol
T =350 K

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∆ Greaction=−187.78−(350 x 172.6
1000 )
∆ Greaction=−187.78− 60410
1000
¿−248.19 k J / mol
d. Find ∆Grxn for the decomposition reaction at 350. K and 100.bar pressure (clearly
justify any assumptions that you make).
∆ Greaction=−RTin ( p 2
p 1 )
¿−109.6
1000 x 350 X in ( 100
1 )
¿−109.6
1000 x 350 X 4.605
¿−38.36 x4.605
¿−176.65 kJ /mol
Increase in pressure of the product it makes ∆ Gand becomes more positive.
2. During class, we used partial derivatives of state functions to find relationships among
different thermodynamic variables. Use that knowledge to
a. Show the dependence of ∆S on p and T. That is, a general mathematical expression that
shows dS in relation with dT and dp.
b. Use that expression to obtain the equation for the dependence of ∆S with pressure for an
ideal gas, at constant Temperature.
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b) For a substance with no residual entropy, at T=0K: S = Cp = , hence it is
to heat matter near absolute zero, that is it requires amount of energy per degree
if Temp rise

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4.

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5.

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6. Use the following phase diagram for Carbon to answer the questions below (Try to be as
quantitative as possible, however a good estimation would be ok).
a. Circle the triple point(s) in the phase diagram, and describe it (them) in terms of: phases
in equilibrium and (P,T ) parameters.
b. What is the normal fusion point of carbon?
c. If you have a sample of Carbon at point c, describe the phase changes that it will undergo
under constant heating to 5,000K
d. Describe the phase changes that C will undergo starting from point d, and compressing it
down to 50 bar
e. What is the minimum pressure you need to convert graphite into a diamond at room
temperature?