Question

The van der Waals equation of state is (P + a(n/V )^2)(V/n − b) = RT, where a and b are gas-specific constants. For Hydrogen gas, a = 2.45 × 10^-2P a · m^6 and b = 26.61 × 10^-6m^3/mol, while for an ideal gas a = b = 0. (a) Consider trying to measure the ideal gas constant in a lab from the relation R = P V/(nT), where P, V, n, and T are all measured parameters. However, your working gas is hydrogen rather than a true ideal gas. Would your measurement of R be more accurate at low density or high density? (b) You try to measure R by measuring the pressure using 2000 moles of Hydrogen in a 1 m^3 volume at room temperature. How far off will your measurement be from the true ideal gas constant, in percentage terms? (c) Calculate the work done on a van der Waals gas to contract it from volume Vi = 2m^3 to Vf = 1m^3.

Answer #1

The amount n = 2.00 mol of a van der Waals gas with a = 0.245 m6
Pa mol-2 occupies a volume of 0.840 L if the gas is at a
temperature of 85.0 K and at a pressure of 2850 kPa. From this
information, calculate the van der Waals constant b and the
pressure p of this gas sample when it occupies a volume of 1.680
dm3 at T = 255 K.

Use the van der Waals equation of state to calculate the
pressure of 2.90 mol of CH4 at 457 K in a 4.50 L vessel. Van der
Waals constants can be found here.
P= ________ atm
Use the ideal gas equation to calculate the pressure under the
same conditions.
P= ______ atm

Derive an expression for the isothermal reversible expansion of
a van der Waals gas. Account physically for the way in which the
coefficients a and b appear in the expression. Using Maple, plot
the expression along with that for an ideal gas. For the van der
Waals gas, use a case first where a = 0 and b = 5.11 x
10-2 mol-1 and where a = 4.2 L2
atm mol-2 and b = 0. Take Vi = 1.0 L,...

For ethane,
C2H6, the van der Waals constants are a =
5.435x10−1 Pa.m6/mol−2 and b =
6.51x10−5 m3/mol
Calculate the pressure exerted by 1.0
mole of ethane and the compression factor Z:
In a 20 L container at 300K as an ideal gas
P = _______________ __________ Z =
___________
In a 20 L container at 300K as a van der Waals gas
P = _______________ __________ Z =
___________
In an 100. mL container at 900 K as an...

Use the van der Waals equation of state to calculate the
pressure of 4.00 mol of Xe at 483 K in a 4.20-L vessel. Van der
Waals constants can be found here.
Use the ideal gas equation to calculate the pressure under the
same conditions.

Use the ideal gas equation and the Van der Waals equation to
calculate the pressure exerted by 1.00 mole of Argon at a volume of
1.31 L at 426 K. The van der Waals parameters a and
b for Argon are 1.355 bar*dm6*mol-2
and 0.0320 dm3*mol-1, respectively. Is the
attractive or repulsive portion of the potential dominant under
these conditions?

The amount 2.00 mol of a van der waals gas with a=0.245 m^6 Pa
mol^-2 occupies a volume of 0.840 L if the gas is at a temperature
of 85k and at a pressure of 2850 kPa. From this information,
calculate the van der waals constant b and pressure p of this
sample when it occupies a volume of 1680 dm^3 at T=255k.

Problem 18.41
For oxygen gas, the van der Waals equation of state achieves its
best fit for a=0.14N⋅m4/mol2 and
b=3.2×10−5m3/mol.
Part A
Determine the pressure in 1.7 mol of the gas at 9 ∘C if its
volume is 0.50 L , calculated using the van der Waals equation.
Express your answer using two significant figures.
Part B
Determine the pressure in 1.7 mol of the gas at 9 ∘C if its
volume is 0.50 L , calculated using the ideal...

How is the Van der Waals equation an improvement over the ideal
gas equation? How are the a and b parameters related to molecular
properties of the gas?

A. Use the van der Waals equation to calculate the pressure
exerted by 1.205 mol of Cl2 in a volume of 4.990 L at a temperature
of 286.5 K .
B. Use the ideal gas equation to calculate the pressure exerted
by 1.205 mol of Cl2 in a volume of 4.990 L at a temperature of
286.5 K .

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