At normal atmospheric pressure of 1.00 atm, solid carbon dioxide (‘dry ice’ ) su

Question

At normal atmospheric pressure of 1.00 atm, solid carbon dioxide (‘dry ice’ ) sublimes directly into a gas at -78.5oC. Given the following data and constants, calculate the amount of heat energy, in Joules, needed to heat an 88.0-gram sample of CO2(s) from -100.0oC to its critical point temperature of 31.0°C.

For Carbon Dioxide;

Part 1:

How many Joules of heat are necessary to warm solid CO2 sample from -100.0oC to -78.5oC?

Part 2:

How many Joules of heat are necessary for the solid CO2 sample to sublime to a gas at -78.5oC?

Part 3:

How many Joules of heat are necessary to warm gaseous CO2 sample from -78.5oC to 31.0oC?

Part 4:

What is the total amount of heat energy, in Joules, needed to heat an 88.0-gram sample of CO2(s) from -100.0oC to its critical point temperature of 31.0°C?

Sorry for the long question. Thanks in advance.

Heat Capacity of Solid, Cs(solid) 52.0 J/mol oC Heat Capacity of Liquid, Cl(liquid) 36.3 J /mol 0C Enthalpy of Sublimation, Hsub 25.0 kJ/mol oC

Explanation / Answer

The following 3 processes are taking place:

1) Rise in temperature of solid CO2 from -100ºC to the sublimation temperature, -78.5ºC. Let the heat energy involved be H1.

2) Sublimation of solid CO2 to gaseous CO2 at the sublimation temperature. Let the heat energy involved be H2.

3) Heating gaseous CO2 from -78.5ºC to its critical temperature, 31ºC. Let the heat energy involved be H3.

First calculate the moles of solid CO2taken = (88.0 g)/(44.0 g/mol) = 2.0 mole (molar mass of CO2 = 44 g/mol). Also, note that the moles of solid and gaseous CO2 will be the same, since we assume no loss due to sublimation. Calculate the energy changes one by one.

1) H1 = (moles of solid CO2)*(heat capacity of solid CO2)*(change in temperature) = (2.0 mole)*(52.0 J/mol.ºC)*[(-78.5ºC) – (-100ºC)] = (2.0 mole)*(52.0 J/mol.ºC)*(-78.5 + 100)ºC = 2236 J (ans).

2) H2 = (moles of solid CO2)*(enthalpy of sublimation) = (2.0 mole)*(25.0 kJ/mol) = (2.0 mole)*(25 kJ/mol)*(1000 J/1 kJ) = 50000 J (ans).

3) H3 = (moles of gaseous CO2)*(heat capacity of gaseous CO2)*(change in temperature) = (2.0 mole)*(heat capacity of gaseous CO2)*[(31.0ºC) – (-78.5ºC)] = (2.0 mole)*(heat capacity of gaseous CO2)*(109.5ºC) = (219.0 mole.ºC)*(heat capacity of gaseous CO2)

Note that we aren’t given the heat capacity of gaseous CO2 (we are given the heat capacity of solid and liquid CO2) and hence we cannot estimate the value.

4) The total heat energy needed will the summation of the heat energy changes for the three processes listed above. Since, we couldn’t estimate H3, we cannot find a value for the total heat energy change, H.

H = H1 + H2 + H3

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