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zhuklara
1 month ago
10

A decorative "ice" sculpture is carved from dry ice (solid CO2) and held at its sublimation point of –78.5°C. Consider the proce

ss in which a CO2 sculpture, weighing 389 g, sublimes on a granite tabletop. The temperature of the granite is 12.0°C and the process occurs reversibly. Assume a final temperature for the CO2 vapor of –78.5°C. The enthalpy of sublimation of CO2 is 26.1 kJ/mol.a. Calculate the entropy of sublimation for carbon dioxide (the system) ___ J/Kmol b. Calculate the entropy of the universe for this reversible process. Use three significant figures in the answer __J/K
Chemistry
1 answer:
lions [2.9K]1 month ago
7 0

Answer:

The responses to the questions are:

a. The entropy of sublimation for CO2 is 134.07 J/Kmol.

b. The entropy for the universe in this reversible scenario is 376 J/K.

Explanation:

Entropy of sublimation refers to the change in entropy that occurs when one mole of a solid transitions to vapor at its sublimation point.

a. The mass of solid CO₂ is noted as 389 g.

The molar mass of CO₂ is 44.01 g/mol.

The number of moles of CO₂ in the sculpture is calculated as: Mass/(Molar mass)

= (389 g)/(44.01 g/mol) = 8.84 moles.

The entropy of sublimation is expressed as

ΔS_{sublimation} = S_{vapor} - S_{solid} = \frac{\Delta H_{sublimation}}{T}

Where:

ΔH_{sublimation}  = 26.1 KJ/mol.

T = Temperature = –78.5°C = ‪194.65‬ K.

Consequently, the energy required for the 389 g of dry ice to sublime is: 26.1 KJ/mol × 8.84 moles = 230.695 KJ.

Subsequently, the entropy of sublimation is calculated as ΔS_{sublimation} = \frac{230.695 KJ}{194.65 K}

= 1.185 KJ/K

= 1185 J/K = 1185/8.84 J/Kmol = 134.07 J/Kmol.

b. The universe’s entropy can be computed as:

ΔS_{universe} = \Delta S_{system} + ΔS_{surrounding}

If the heat absorbed by the system equals the heat released by the surroundings, then:

ΔS_{universe} = \frac{Q}{ T_{system}}  -\frac{Q}{T_{surrounding}}

                =1.185 KJ/K - -\frac{230.695 KJ}{285.15K} = 1.185 KJ/K - 0.809 KJ/K = 0.376 KJ/K

= 376 J/K.

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