Question

What would be the change in entropy (if the change is zero, explain why, if not then calculate) when one mixes the following gases, at a temperature of 1000K and room pressure, if the gases are:

a) A mole of H with another mole of H.

b) A mole of gaseous C_{12} with a mole of gaseous
C_{13}.

Answer #1

The effect is the same as allowing each gas to expand to twice its volume; the thermal energy in each is now spread over a larger volume.

This question is imprecisely stated. I assume that for case (a),
your teacher is implicitly assuming that the isotopic composition
of both samples of hydrogen (which would normally exist as H2
molecules, not as individual H atoms) have identical isotopic
compositions. (Remember that natural hydrogen is composed of two
isotopes, protium, or H-1, and deuterium, H-2. Tritium, H-3, has a
vanishingly small natural abundance on Earth).

I am also assuming that this mixing occurs at a constant volume (as
well as pressure and temperature).

With the above assumption, the entropy change for case (a) is zero,
because the particles in "parcel 1) of the hydrogen are
indistinguishable from the particles in "parcel 2" of the hydrogen.
Another way of thinking of this is that the average density of
protium and deuterium atoms in the system does not change when the
two parcels of gas are mixed. This is a version of the Gibbs'
paradox. The key here is that the particles that are mixing in the
two parcels are indistinguishable from one another.

In case (b), we clearly have distinguishable particles. The entropy
of mixing is most easily calculated from the standard formula for
the entropy of mixing:

ΔS_mix = -n*R*[x1*ln(x1) + x2*ln(x2)]

where x1 and x2 are the mole fractions of components 1 and 2 in the
mixture, n is the total number of moles involved, and R is the
universal gas constant. For a 2-component mixture (as we have here)
x2 = 1 - x1. Specifically, in this case, x1 = x2 = 0.5, and n = 1
mole

The entropy of mixing in this case is therefore:

ΔS_mix = -1mol*R*[0.5*ln(0.5) + 0.5*ln(0.5)] = R*ln(2)*mol = 5.763
J/K

Two different gases A and B are mixed. Calculate change of
entropy.
a) Assume pressure and temperature of A and B are the same.
b) Now assume pressure and temperature of A and B are different.
The system is
thermally isolated. Calculate entropy and final temperature,
Tf.

Calculate the change in entropy for one mole of ideal gas which
expands from an initial volume of 2 L and initial temperature of
500 K to a final volume of 6 L under the following conditions.
P(initial) refers to the pressure when T(initial)= 500K,
V(initial)= 2 L.
a) Irreversible expansion against a constant pressure of
Pinitial/2
b) Irreversible expansion against a vacuum...a 'free
expansion'.
c) Adiabatic irreversible expansion against a constant pressure
of Pfinal
d) Adiabatic reversible expansion

The change in entropy of the system and the universe if one mole
of argon is expanded isothermally and reversible at 300. K from
10.0 L to 20.0 L.
assuming the expansion is free.
Calculate:
a) entropy of the system in J/K
b) entropy of the universe in J/K
Please explain each step.

calculate the molar entropy change when (a) water and (b)
benzene are evaporated at their boiling points at a pressure of 1
atm. what are the entropy changes in (i) the system, (ii) the
surroundings, and (iii) the universe, in each case?

For each case determine the change in entropy for
the surroundings and the universe, when 1 mole of a
diatomic gas expands from its initial volume of 5 L and 31.5 ◦C
to:
CASE (a) a final volume of 25 L reversibly and
isothermically.
CASE (b) irreversibly and isothermically against an external
pressure of 1 atm.
CASE (c) a final volume of 25 L reversibly and adiabatically.
Yes, it is zero, but you have to demonstrate it.
CASE (d) irreversibly...

Explain why
A) If heat flows from high to low temperatures, the entropy
change in any process cannot be negative.
B) The specific heat of any substance is always lowest in the
vapor (gas) phase.

Aluminum nitride (AlN), is a wide band-gap semiconductor
material and has use in opto- electronics. It can be formed by
reacting metallic aluminum with pure, gaseous nitrogen (N2).
(a) Write the chemical reaction for the formation of one mole of
Aluminum Nitride.
(b) What is the change in enthalpy (∆H) if all the
reactants and products are at 298 K and 1 atm pressure?
(c) What is the change in entropy (∆S) for the reaction
if all the reactants and...

Here we calculate the partition function, molar translational
internal energy, and molar translational entropy of a monatomic
gas. The single particle translational partition function is
qtrans=VΛ3) where Λ is the thermal wavelength and teh entropy is
given by the Sackur-Tetrode equation
S=N*kB*ln((qtrans*e^5/2)/N).
A. Calculate the single particle translational partition
function q for neon gas at T=298K and V=22.4L. Assume neon behaves
ideally.
B. Based on your answer in Part A, calculate the molar
translational internal energy of neon at at...

One mole of either carbon monoxide or benzene are completely
combusted with oxygen at constant temperature and pressure (298 K
and 1 atm) to generate CO2 and H2O. Assume all substances are ideal
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a. Write out balanced combustion reactions for each
reaction.
b. Calculate the change in entropy for the system for each
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c. Use the enthalpies of formation to calculate the heat lost or
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d....

In which of the following would the electric field be zero?
Please explain why it is zero or it isn't
a) in a region with no charges
b) in a region with a constant magnetic field.
c) in an ideal conductor.

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