29 Jul WHAT MASS OF WATER SHOULD BE EVAPORATED EACH DAY TO MAINTAIN CONSTANT TEMPERATURE?
Chem 113A Homework #1
Due: Tues. 10/14/14
1. A sample of propane (C3H8) placed in a closed vessel together with an amount of O2 that is 3.00 times
the amount needed to completely oxidize the propane to CO2 and H2O at constant temperature.
Calculate the mole fraction of each component in the resulting mixture after oxidation assuming that
the H2O is present as a gas.
2. Liquid N2 has a density of 875.4 kg m–3 at its normal boiling point. What volume does a balloon
occupy at 18.5ºC and a pressure of 1.00 atm if 2.00 x 10–3 L of liquid N2 is injected into it?
3. A gas sample is known to be a mixture of ethane and butane. A bulb of 200.0 cm3 capacity is filled
with the gas to a pressure of
at 20.0ºC. If the weight of the gas in the bulb is 0.3846
g, what is the mole percent of butane in the mixture
4. The total pressure of a mixture of oxygen and hydrogen is 1.00 atm. The mixture is ignited and the
water is removed. The remaining gas is pure hydrogen and exerts a pressure of 0.400 atm when
measured at the same values of T and V as the original mixture. What was the composition of the
original mixture in mole percent?
5. Calculate the pressure exerted by Ar for a molar volume 1.42 L at 300 K using the van der Waals
equation of state. The van der Waals parameters a and b for Ar are1.355 bar dm6 mol–2 and 0.0320
dm3 mol–1, respectively. Is the attractive or repulsive portion of the potential dominant under these
conditions?
6. The equation of state of a certain gas is given by p = RT/Vm + (a+bT)/Vm2, where a and b are
constants. Find (Vm/T)p.
7. 3.00 moles of an ideal gas at 27.0 ºC expands isothermally from an initial volume of 20.0 dm3 to a
final volume of 60.0 dm3. Calculate w for this process a) for expansion against a constant external
pressure of
and b) for a reversible expansion.
8. An ideal gas described by Ti = 300 K, Pi = 1.00 bar, and Vi = 10.0 L is heated at constant volume until
P = 10.0 bar. It then undergoes a reversible isothermal expansion until P = 1.00 bar. It is then restored
to its original state by the extraction of heat at constant pressure. Depict this closed-cycle process in a
P-V diagram. Calculate w for each step and for the total process. What values for w would you
calculate if the cycle were traversed in the opposite direction?
9. A pellet of Zn of mass 10.0 g is dropped into a flask containing dilute H2SO4 at a pressure of P = 1.00
bar and temperature T = 298 K. What is the reaction that occurs? Calculate w for the process.
10. 1 mol of an ideal gas for which
is heated from an initial temperature of 0ºC
to a final temperature of 275ºC at constant volume. Calculate q, w, U, and H for this process.
11. Calculate U and H for the transformation of 1 mole of an ideal gas from 27.0ºC and 1.00 atm to
327ºC and 17.0 atm if
in units of
.
12. One mole of N2 in a state defined by Ti = 300 K and Vi = 2.50 L undergoes an isothermal reversible
expansion until Vf = 23.0 L. Calculate w assuming the gas is ideal.
13. An average human produces about 10 MJ of heat each day through metabolic activity. If a human
body were an isolated system of mass 65 kg with the heat capacity of water, what temperature rise
would the body experience? Human bodies are actually open systems, and the main mechanism of
heat loss is through the evaporation of water. What mass of water should be evaporated each day to
maintain constant temperature?
14. Suppose that a 10 kg mass of iron at 20 C is dropped from a height of 100 meters. What is the
kinetic energy of the mass just before it hits the ground? What is its speed? What would the final
temperature of the iron if all its kinetic energy is transformed into internal energy? Take the molar
heat capacity of iron to be
and the gravitational acceleration constant to be
.
15. Calculate the work involved in the reversible isothermal expansion of one mole of CH4(g) from a
volume of
to
at 300 K. In this problem assume methane is a van der
Waals gas.
16. Calculate the minimum work required to compress 5.00 moles of an ideal gas isothermally at 300 K
from a volume of
to
.
17. Consider the Peng-Robinson equation of state:
where α and β are the gas-specific parameters. Derive and expression for the reversible isothermal
work of expansion for a Peng-Robinson gas.
18. One mole of ethane at 25 C and one atm is heated to 1200 C at constant pressure. Assuming ideal
behavior, calculate the values of
and
given that the molar heat capacity of ethane is
given by
19. Repeat the calculation performed in problem 18 for a constant-volume transformation instead of
constant pressure.
20. Compare the pressures calculated using the ideal gas law, the van der Waals equation, the PengRobinson equation of state (see problem 17), and the Redlich-Kwong equation of state (see below)
for propane at 400K and a density of
with the value of 400 bar measured
experimentally. The Peng-Robinson parameters for propane are:
and
. The Redlich-Kwong equation of state is given by:
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