Consider 1.000 g of oxygen gas molecules in a container having a fixed volume of
ID: 1022027 • Letter: C
Question
Consider 1.000 g of oxygen gas molecules in a container having a fixed volume of 10.00 mL at a temperature of 298 K. The molecular weight of oxygen is MW(O2) = 32.00 g/mol.
(a) Assuming that O2 behaves as an ideal gas, calculate the pressure of O2 at these conditions.
(b)What is the standard enthalpy of formation of O2(g)? Is this defined by a law of thermodynamics (e.g. lst, 2nd, or 3rd laws)? If so, please state the law. If not, please state why not. Briefly explain your answer in 1-2 sentences.
(c) What is the internal energy U of O2 gas in the container, treating the gas as ideal (i.e. point-like)? What is the molar specific heat capacity cv at constant volume of O2 gas in the container if you include rotational degrees of freedom that are appropriate for a linear diatomic molecule?
(d) Assuming that O2 behaves ideally (molar specific heat capacity is cv = 3R/2), what is the entropy change S as a result of heating the gas at constant volume from 298 K to 455 K?
Explanation / Answer
Volume = 10 ml at 298 K
PV= nRT or p= n R T/V or 1/32 x .08314 x 298/0. .001 = 774.2413 Bar
The pressure of O2 at the given conditions will be 774.2413 Bar.
(b)The standard enthalpy of formation is, the change of enthalpy when one mole of a substance in its standard state is formed from its elements under standard state conditions of 1 atmosphere pressure and 298K temperature.
Oxygen gas consists of its elements (Oxygen atom) already in standard state, so there is not any change here. Therefore standard enthalpy of formation for Oxygen gas at the given standard state is zero.
(c)Oxygen is a diatomic molecules. For such molecule at 298K, the translational and rotational motion of the molecule contribute to specific heat and therefore Cv = 3R/2
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