7. Gases

Van der Waals Equation

0048 - van der Waals Equation of State

Van der Waals Equation of State

Calculate the pressure that CCl4 will exert at 80 °C if
1.00 mol occupies 33.3 L, assuming that (a) CCl4 obeys the
ideal-gas equation (b) CCl4 obeys the van der Waals equation. (Values for the van der Waals constants are given in Table 10.3.)

The graph below shows the change in pressure as the temperature
increases for a 1-mol sample of a gas confined to a
1-L container. The four plots correspond to an ideal gas and
three real gases: CO2, N2, and Cl2. (a) At room temperature,
all three real gases have a pressure less than the ideal gas.
Which van der Waals constant, a or b, accounts for the influence
intermolecular forces have in lowering the pressure of a
real gas? 
<img src="https://lightcat-files.s3.amazonaws.com/problem_images/334e4e5d2347654f-1664296816343.jpg" alt="" />

It turns out that the van der Waals constant b equals four 
times the total volume actually occupied by the molecules 
of a mole of gas. Using this figure, calculate the fraction of 
the volume in a container actually occupied by Ar atoms 
(b) at 20.27 MPa pressure and 0 °C. (Assume for 
simplicity that the ideal-gas equation still holds.)

Use the van der Waals equation and the ideal gas equation to
calculate the volume of 1.000 mol of neon at a pressure of
500.0 atm and a temperature of 355.0 K. Explain why the two
values are different. (Hint: One way to solve the van der Waals
equation for V is to use successive approximations. Use the
ideal gas law to get a preliminary estimate for V.)

The graph below shows the change in pressure as the temperature
increases for a 1-mol sample of a gas confined to a 1-L container. The four plots correspond to an ideal gas and three real gases: CO2, N2, and Cl2. (b) Use the van der Waals constants in Table 10.3 to
match the labels in the plot (A, B, and C) with the respective
gases 1CO2, N2, and Cl22.
<img src="https://lightcat-files.s3.amazonaws.com/problem_images/b0aad07fcef40e62-1676487074693.jpg" alt="" />

A steel container with a volume of 500.0 mL is evacuated, 
and 25.0 g of CaCO3 is added. The container and contents 
are then heated to 1500 K, causing the CaCO3 to decompose 
completely, according to the equation 
CaCO31s2¡CaO1s2 + CO21g2. 
(b) Now make a more accurate calculation of the pressure 
inside the container. Take into account the volume of 
solid CaO 1density = 3.34 g/mL2 in the container, and 
use the van der Waals equation to calculate the pressure. 
The van der Waals constants for CO21g2 are 
a = 3.59 1L2 # atm2>mol2 and b = 0.0427 L>mol.

Use the van der Waals equation and the ideal gas equation to
calculate the pressure exerted by 1.000 mol of Cl2 in a volume of
5.000 L at a temperature of 273.0 K. Explain why the two values
are different.

The van der Waals equation explained

Consider the following gases, all at STP: Ne, SF6, N2, CH4.
(d) Which one has the highest total molecular volume relative to the space occupied by the gas?

Real Gases and the van der Waals Equation Explained

Non-Ideal Gases and the Van der Waals Equation

Consider the following gases, all at STP: Ne, SF6, N2, CH4. 
(g) Which one would have the largest van der Waals b parameter?

van der Waal's Equation for NON-Ideal Gases

The Rankine temperature scale used in engineering is to the 
Fahrenheit scale as the Kelvin scale is to the Celsius scale. 
That is, 1 Rankine degree is the same size as 1 Fahrenheit 
degree, and 0 °R = absolute zero. 
(b) What is the value of the gas constant R on the Rankine 
scale in 1L ~ atm2>1°R ~ mol2? 
(c) Use the van der Waals equation to determine the pressure 
inside a 400.0-mL vessel that contains 2.50 mol of 
CH4 at a temperature of 525 °R. For CH4, a = 2.253 
1L2 ~ atm2>mol2 and b = 0.04278 L>mol.

Which gaseous compound is expected to have the largest value for the Van der Waals constant b? a) O2b) CH3CH3c) HBrd) S8e) Ne

Table 10.3 shows that the van der Waals b parameter has
units of L/mol. This means that we can calculate the sizes
of atoms or molecules from the b parameter. Refer back to
the discussion in Section 7.3. Is the van der Waals radius we
calculate from the b parameter of Table 10.3 more closely
associated with the bonding or nonbonding atomic radius
discussed there? Explain.

Based on their respective van der Waals constants
( Table 10.3), is Ar or CO2 expected to behave more nearly
like an ideal gas at high pressures?

Which statement concerning the van der Waals constants a
and b is true?
(a) The magnitude of a relates to molecular volume,
whereas b relates to attractions between molecules.
(b) The magnitude of a relates to attractions between
molecules, whereas b relates to molecular volume.
(c) The magnitudes of a and b depend on pressure.
(d) The magnitudes of a and b depend on temperature.

Van der Waals Equation Example 1

Real vs Ideal Gases & the van der Waals Equation - AP Chemistry Complete Course - Lesson 24.4

Large amounts of nitrogen gas are used in the manufacture 
of ammonia, principally for use in fertilizers. Suppose 
120.00 kg of N21g2 is stored in a 1100.0-L metal cylinder 
at 280 °C. (b) By using the data in Table 10.3, 
calculate the pressure of the gas according to the van der 
Waals equation.

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[BOOK CHEM] Clutch Version

Partial Pressure

Partial Pressure (PGas) is the pressure exerted by an individual gas within a container.

Velocity Distributions

Velocity Distributions represent probability distributions for a gas when examining their molar mass and temperature.

Mole Fraction

Mole Fraction (X) represents the mole component by total moles.&nbsp;

Mole Fraction -

The Ideal Gas Law Derivations

The&nbsp;Ideal Gas Law Derivations are a convenient way to solve gas calculations involving 2 sets of the same variables.&nbsp;

Root Mean Square Speed

Root Mean Square Speed&nbsp;allows for the determination of the velocity of 1 type of gas molecule.

The Ideal Gas Law: Density

Under certain conditions of pressure and temperature, the Ideal Gas Law can determine the density&nbsp;of a gas.&nbsp;

Effusion

Effusion is the escaping of gas molecules or atoms through a pinhole.&nbsp;

Kinetic Energy of Gases

Kinetic Energy is the energy an object possesses due to its motion.

Gas Stoichiometry

Gas Stoichiometry involves chemical reactions that contain gases.

The Ideal Gas Law

The Ideal Gas Law formula relates the behavior of gases under varying conditions of pressure, volume, moles and temperature.

Chemistry Gas Laws: Combined Gas Law

The Combined Gas Law&nbsp;is created from “combining” Boyle’s Law, Charles’ Law, and Gay–Lussac’s Law.

Pressure Units

Pressure is the force that is exerted within a given volume of space.&nbsp;

Kinetic Molecular Theory

A gas is seen as a collection of molecules or individual atoms that are in constant motion. The Kinetic-Molecular Theory tries to use data of real gases to predict how an ideal gas would behave if they existed.&nbsp;&nbsp;

Standard Temperature and Pressure

In order to accurately study the effect that changes in pressure, temperature and moles have on volume, chemists will often run their experiments under Standard Temperature and Pressure.&nbsp;

The Ideal Gas Law Applications

The Ideal Gas Law Applications establish both the direct and inverse relationships between the Ideal Gas Law variables.

Maxwell-Boltzmann Distribution

The Maxwell-Boltzmann Distribution is a probability distribution curve that describes the speed of a gas at a specific temperature.

Chemistry Gas Laws

Chemistry Gas Laws&nbsp;are laws that relate together the pressure, volume and temperature of a gas.

The Ideal Gas Law: Molar Mass

The Ideal Gas Law can be further extended to find the molar mass of a gas.&nbsp;

The&nbsp;Van der Waals Equation is used when dealing with real, non-ideal gases.&nbsp;

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