Question

A gas is said to behave like an ideal gas when the relation $PV/T=$ constant. When do you expect a real gas to behave like an ideal gas? (a) When the temperature is low (b) When both the temperature and pressure are low (c) When both the temperature and pressure are high (d) When the temperature is high and pressure is low

Short answer

The correct answer is (d). A real gas is expected to behave like an ideal gas when the temperature is high and the pressure is low.

Step-by-step solution

Understanding when gases behave ideally

Ideal gas behavior is seen when the particles of the gas do not interact much with each other. This condition is fulfilled when the gases are at a high temperature and low pressure because under these conditions the particles of the gas are far apart from each other. Therefore, they do not attract or repel each other significantly.

Analyzing the options

Option (d) states 'When the temperature is high and pressure is low'. This option matches our analysis from Step 1 that gases behave ideally under conditions of high temperature and low pressure.

Key concepts

Real Gas

In real life, gases don't always behave exactly like the ideal gas model predicts. Real gases have particles that do interact with each other. These interactions include attracting or repelling each other, which can affect how the gas behaves.

• Real gases deviate from ideal behavior because of intermolecular forces and finite atomic or molecular volumes.
• At high pressures, particles are much closer and their volume becomes significant compared to the total volume of the gas.
• At low temperatures, attractive forces can cause gas particles to stick together, leading to condensation.

Understanding these concepts helps in knowing why real gases don't always follow the ideal gas laws under certain conditions.

Gas Laws

Gas laws are the principles that describe how gases behave under various conditions of temperature, pressure, and volume. There are several key gas laws, each explaining different aspects of gas behavior.

• Boyle's Law: States that pressure and volume are inversely proportional when temperature is constant. This means if you increase pressure, volume decreases and vice versa.
• Charles's Law: Indicates that volume and temperature are directly proportional when pressure is constant. So, increasing temperature will increase volume.
• Avogadro's Law: Shows that volume and number of moles are directly proportional at constant temperature and pressure.

These laws combine into the ideal gas law, represented as $$PV=nRT$$ where $P$ is pressure, $V$ is volume, $n$ is number of moles, $R$ is the gas constant, and $T$ is temperature. This law is best applied to situations where gases behave ideally.

Temperature and Pressure Effects

Temperature and pressure have significant impacts on how gases behave. These factors determine how closely gas molecules are packed together and how much they interact.

• High temperatures give gas molecules more energy, causing them to move faster and collide with greater force. This helps to reduce the effect of intermolecular attractions.
• At low pressures, gas particles are farther apart and this reduces the impact of forces between the particles.
• Low temperatures slow down particles, making intermolecular forces more noticeable and sometimes causing gases to liquefy.
• High pressures push particles closer, making their finite size and attractions more important.

For gases to behave more like an ideal gas, high temperature and low pressure are the best conditions.

Ideal Gas Conditions

Ideal gas conditions refer to specific situations where gases perfectly follow the ideal gas law, without deviations caused by particle interactions or volume.

• When the temperature is high, kinetic energy dominates over intermolecular forces thus minimizing interactions.
• Low pressure ensures particles are spread out, making their volume negligible in comparison to the container's volume.
• These conditions are unrealistic for most real gases at everyday environments but are approached in controlled settings such as many scientific experiments.
• Under these ideal gas conditions, gases behave predictably as described by the ideal gas law.

By understanding when and why gases meet these conditions, predictions about gas behavior become more accurate, helping in applications ranging from weather prediction to industrial chemical processes.