Problem 106 - Chemistry Matter and Change

Question

Infer At very high pressures, will the ideal gas law calculate a pressure that is higher or lower than the actual pressure exerted by a sample of gas? How will the calculated pressure compare to the actual pressure at low temperatures? Explain your answers.

Step-by-Step Solution

Answer

The ideal gas law calculates lower pressure at high pressures and higher pressure at low temperatures.

Step 1: Understanding the Ideal Gas Law

The ideal gas law is given by the equation \( PV = nRT \), where \( P \) is pressure, \( V \) is volume, \( n \) is the number of moles, \( R \) is the gas constant, and \( T \) is temperature. This equation assumes that gas particles do not attract or repel each other and that they occupy no volume.

Step 2: Analyzing High-Pressure Conditions

Under very high pressures, the assumptions of the ideal gas law become less valid. Gas particles are forced closer together, increasing intermolecular forces and reducing the volume available to the particles. The equation therefore overestimates the volume available, leading to a calculated pressure that is lower than the actual pressure exerted by the gas.

Step 3: Analyzing Low-Temperature Conditions

At low temperatures, gas molecules move more slowly, which means intermolecular forces become more significant. These forces cause the gas to behave non-ideally, resulting in an attractive force that decreases the volume effectively occupied by the gas molecules. As a result, the ideal gas law predicts a pressure that is higher than the actual pressure because it does not account for these intermolecular attractions.

Key Concepts

Non-ideal Gas Behavior

Gases often deviate from the ideal conditions assumed in the ideal gas law. In reality, gas particles have volume and interact through intermolecular forces. These deviations are referred to as non-ideal gas behavior. The ideal gas law assumes that gases behave perfectly, with no interactions between molecules and with the particles occupying no space. However, this is not always the case.

At extreme conditions, such as high pressures or low temperatures, these assumptions no longer hold true. In such cases, the behavior of gases must be described by more complex equations, such as the van der Waals equation, that account for both the finite volume of gas particles and the forces between them.

Intermolecular Forces

Intermolecular forces are forces of attraction or repulsion between individual molecules. These forces become significant at conditions where gas deviations from ideal behavior are evident.

There are various types of intermolecular forces, including:

• Van der Waals forces: Weak forces that occur between all molecules, arising from temporary dipoles.
• Dipole-Dipole forces: Occur between polar molecules with permanent dipoles.
• Hydrogen bonds: Strong dipole-dipole attractions occurring in molecules where hydrogen is directly bonded to a highly electronegative atom like nitrogen, oxygen, or fluorine.

At low temperatures, molecules move more slowly, allowing these forces to have a greater impact on how gases behave, causing non-ideal behavior.

High Pressure Effects

When gases are at high pressure, molecules are pushed closer together, increasing the effect of intermolecular forces. Under these conditions, the volume available to the gas particles is less than what is predicted by the ideal gas law.

The ideal gas law often underestimates the pressure because it does not account for these interactions. At high pressures, real gases exhibit a higher pressure than predicted because the particles experience higher intermolecular forces when they are so compressed. This results in the real pressure being higher than the pressure calculated by the ideal gas law under these conditions.

Low Temperature Effects

Low temperatures cause gas molecules to slow down, enhancing the effect of intermolecular attractions. The slower movement allows for attractive forces to take effect, causing the gas molecules to condense more than they would under ideal conditions.

These increased attractions mean that the space gases actually occupy is less than expected. The ideal gas law does not consider these attraction forces, thus leading it to predict a pressure higher than the actual measured pressure. This is because the real gas effectively occupies a smaller volume than an ideal gas would, resulting in a lower actual pressure.