26 Jun At the end of the process, the pressure is
Question
Chem 113A Homework #2
Due: Tues. 10/21/14
1. 1 mol of an ideal gas with
initially at 298 K and
undergoes a
reversible adiabatic compression. At the end of the process, the pressure is
.
Calculate the final temperature of the gas. Calculate
and
for this process.
2. Use the relation
along with the Euler chain relation and the
inversion rule to obtain an expression for the internal pressure
in terms of P, α, T
and κ.
3. A mass of 25.5 g of H2O(g) at 373 K is mixed with 325 g of H2O(l) at 285 K and 1 atm.
Calculate the final temperature of the system once equilibrium has been reached. Assume
that
for H2O is constant at its values for 298 K throughout the temperature range of
interest.
4. Derive the following expression for calculating the isothermal change in the constant volume
heat capacity:
5. For a gas that obeys the equation of state
Derive the result
6. Show that
for an ideal and a van der Waals gas.
7. Calculate the standard enthalpy of formation of FeS2(s) at 300ºC from the following data at
25ºC. Assume that the heat capacities are independent of temperature. You are also given
that for the reaction 2FeS2 (s) + 11/2O2 (g) → Fe2O3(s) + 4 SO2(g),
8. Several reactions and their standard reaction enthalpies at 298.15 K are given here:
The standard enthalpies of combustion of graphite and C2H2(g) are –393.51 and –1299.58 kJ
mol–1, respectively. Calculate the standard enthalpy of formation of CaC2(s) at 25ºC
9. From the following data, calculate
for the reaction
Values for
for the first two reactions are at 298.15 K, and for the third reaction at 391.4
K. The relevant heat capacities are given in the table below.
10. The total surface area of the earth consisting of forest, cultivated land, grassland and desert is
. Every year, the mass of carbon fixed by photosynthesis by vegetation
covering this land surface according to the reaction
is about
. Calculate the annual enthalpy change resulting
from photosynthetic carbon fixation over the land surface given above. Assume P = 1 bar
and T = 298.15 K.
11. The speed of sound in a gas of molar mass is related to the ratio of heat capacities by
the equation
. Show that
where is the mass density of
the gas. Calculate the speed of argon at 25 °C.
12. The temperature of 1 mol of an ideal gas increases from 18.0º to 55.1ºC as the gas is
compressed adiabatically. Calculate
, and
for this process assuming that
.
13. Liquid sodium is being considered as an engine coolant. How many grams of sodium are
needed to absorb 1.0 MJ of heat if the temperature of the sodium is not to increase by more
than 10 ºC? Take
for liquid Na and
for liquid
.
14. A nearly flat bicycle tire becomes noticeably warmer after it has been pumped up.
Approximate this process as a reversible adiabatic compression. Take the initial pressure and
temperature of the air before it is put in the tire to be
and
. The
final volume of the air in the tire is
and the final pressure is
.
Calculate the final temperature of the air in the tire. Assume that
.
15. It is possible to obtain general relation between
and
using the mathematical formalism
discussed in lecture. Start by considering U as a function of p and T {i.e. U = U(p,T)} and
write
(1)
We could also consider U as a function of V and T {i.e. U = U(V,T)} and write
(2)
Now take V = V(p,T) and substitute its expression for dV into Equation 2 to obtain
(3)
Compare this result with Equation 1 to obtain
(4)
and
(5)
Last, substitute U = H – pV into the left side of Equation 5 and the definitions of
to obtain
and
(6)
Show that
if
, as it is for an ideal gas.
16. Following the procedure of problem 14 and using H = H(p,T) and p = p(V,T) show that
17. Assume that a human requires 2500 calories of energy each day for metabolic activity. What
mass of sucrose
or what mass of ethanol
is needed to provide this
energy?
Note that the “calorie” used in nutrition is actually a kilocalorie.
18. At 25C,
for ethanol. Determine
at 273K given
for the liquid and
for the gas.
19. Because V is a state function
Use this to show that the isothermal compressibility and the isobaric expansion coefficient
are related by
20. Derive the following relation
for the internal pressure of a gas that obeys the Redlich-Kwong equation of state
You will need to recall that the internal pressure is given by
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