At 100 C Which Gas Sample Exerts The Greatest Pressure

At 100°C, the gas sample that exerts the greatest pressure depends heavily on the number of moles of the gas present and the volume it occupies, as described by the Ideal Gas Law. Understanding this principle requires a deep dive into gas behavior, intermolecular forces, and the fundamental relationships governing pressure, volume, temperature, and the number of moles.

Understanding the Ideal Gas Law

The Ideal Gas Law, expressed as PV = nRT, serves as the cornerstone for predicting gas behavior. Here's a breakdown:

P: Pressure (typically in atmospheres, atm, or Pascals, Pa)
V: Volume (typically in liters, L)
n: Number of moles of gas
R: Ideal gas constant (approximately 0.0821 L·atm/mol·K or 8.314 J/mol·K, depending on the units used for pressure and volume)
T: Temperature (in Kelvin, K)

From this equation, we can directly infer that pressure is directly proportional to the number of moles (n) and temperature (T), and inversely proportional to volume (V). In simpler terms:

More gas (higher n) = Higher pressure, if V and T are constant.
Higher temperature (higher T) = Higher pressure, if V and n are constant.
Smaller volume (lower V) = Higher pressure, if n and T are constant.

Factors Influencing Gas Pressure at 100°C

When comparing different gas samples at a constant temperature of 100°C (373.15 K), the key factors that determine which sample exerts the greatest pressure are:

Number of Moles (n): The quantity of gas is the most significant factor. A gas sample with a greater number of moles will exert a higher pressure, assuming volume and temperature are constant.
Volume (V): The space in which the gas is contained plays a critical role. If different gas samples with the same number of moles are present, the one with the smallest volume will exhibit the highest pressure.
Type of Gas: While the Ideal Gas Law assumes that all gases behave identically, real gases deviate from this ideal behavior to varying extents. The van der Waals equation provides a more accurate representation by accounting for intermolecular forces and the volume occupied by gas molecules themselves:

(P + a(n/V)^2) (V - nb) = nRT

Here:
- a represents the attraction between molecules (intermolecular forces).
- b represents the volume excluded by a mole of gas molecules.
Gases with stronger intermolecular forces (higher a value) will exhibit slightly lower pressures than predicted by the Ideal Gas Law. Similarly, gases with larger molecular sizes (higher b value) will also show deviations. However, at moderate pressures and high temperatures like 100°C, these deviations are often small, and the Ideal Gas Law provides a reasonable approximation.

Scenarios and Examples

To illustrate the relationship between these factors and gas pressure, let's consider several scenarios:

Scenario 1: Equal Volumes and Different Numbers of Moles

Suppose we have three gas samples in identical 10-liter containers at 100°C:

Sample A: 0.5 moles of Helium (He)
Sample B: 1.0 moles of Nitrogen (N₂)
Sample C: 1.5 moles of Argon (Ar)

Using the Ideal Gas Law (P = nRT/V), we can calculate the pressure for each sample:

Sample A: P = (0.5 mol * 0.0821 L·atm/mol·K * 373.15 K) / 10 L = 1.53 atm
Sample B: P = (1.0 mol * 0.0821 L·atm/mol·K * 373.15 K) / 10 L = 3.06 atm
Sample C: P = (1.5 mol * 0.0821 L·atm/mol·K * 373.15 K) / 10 L = 4.59 atm

In this scenario, Sample C (Argon with 1.5 moles) exerts the greatest pressure because it has the highest number of moles.

Scenario 2: Equal Numbers of Moles and Different Volumes

Now, consider three gas samples, each containing 0.8 moles of Oxygen (O₂) at 100°C, but in different volumes:

Sample D: 5-liter container
Sample E: 10-liter container
Sample F: 15-liter container

Calculating the pressure for each:

Sample D: P = (0.8 mol * 0.0821 L·atm/mol·K * 373.15 K) / 5 L = 4.91 atm
Sample E: P = (0.8 mol * 0.0821 L·atm/mol·K * 373.15 K) / 10 L = 2.45 atm
Sample F: P = (0.8 mol * 0.0821 L·atm/mol·K * 373.15 K) / 15 L = 1.64 atm

Here, Sample D (Oxygen in the 5-liter container) exerts the greatest pressure due to its smaller volume.

Scenario 3: Different Gases, Moles, and Volumes

Let's introduce more complexity with different gases, numbers of moles, and volumes:

Sample G: 0.3 moles of Hydrogen (H₂) in a 2-liter container
Sample H: 0.6 moles of Carbon Dioxide (CO₂) in a 5-liter container
Sample I: 0.9 moles of Methane (CH₄) in a 8-liter container

The pressure calculations are as follows:

Sample G: P = (0.3 mol * 0.0821 L·atm/mol·K * 373.15 K) / 2 L = 4.59 atm
Sample H: P = (0.6 mol * 0.0821 L·atm/mol·K * 373.15 K) / 5 L = 3.68 atm
Sample I: P = (0.9 mol * 0.0821 L·atm/mol·K * 373.15 K) / 8 L = 3.44 atm

In this case, Sample G (Hydrogen in the 2-liter container) exerts the highest pressure, showcasing the combined effect of a relatively high number of moles and a small volume.

Scenario 4: Considering Real Gas Behavior

While the Ideal Gas Law provides a good approximation, let's briefly consider the impact of real gas behavior using the van der Waals equation. Suppose we have two gases at 100°C in identical 10-liter containers, each with 1 mole:

Sample J: Helium (He), with a = 0.034 atm·L²/mol² and b = 0.0237 L/mol
Sample K: Ammonia (NH₃), with a = 4.17 atm·L²/mol² and b = 0.0371 L/mol

Using the van der Waals equation:

For Sample J (Helium):

(P + 0.034 (1/10)^2) (10 - 10.0237) = 1 * 0.0821 * 373.15*

(P + 0.00034) (9.9763) = 30.64

P ≈ 3.06 atm (The correction is very small for Helium)
For Sample K (Ammonia):

(P + 4.17 (1/10)^2) (10 - 10.0371) = 1 * 0.0821 * 373.15*

(P + 0.0417) (9.9629) = 30.64

P ≈ 3.04 atm (The pressure is slightly lower due to stronger intermolecular forces)

In this scenario, the difference in pressure is small, but it illustrates that gases with stronger intermolecular forces (higher a value) will exhibit slightly lower pressures under real conditions.

The Role of Kinetic Molecular Theory

The Ideal Gas Law is derived from the Kinetic Molecular Theory of gases, which posits the following:

Gases consist of a large number of particles (atoms or molecules) that are in constant, random motion.
The volume of the individual particles is negligible compared to the total volume of the gas.
Intermolecular forces between gas particles are negligible.
Collisions between gas particles and the walls of the container are perfectly elastic (no energy is lost).
The average kinetic energy of the gas particles is directly proportional to the absolute temperature of the gas.

At 100°C, the average kinetic energy of gas particles is relatively high, leading to more frequent and forceful collisions with the container walls. This increased collision rate and force directly contribute to the pressure exerted by the gas.

How to Determine Which Gas Exerts the Greatest Pressure

To definitively determine which gas sample exerts the greatest pressure at 100°C, follow these steps:

Gather Information: Obtain the number of moles (n) and volume (V) for each gas sample. Ensure the temperature is constant at 100°C (373.15 K).
Apply the Ideal Gas Law: Use the formula P = nRT/V to calculate the pressure for each gas sample. Use consistent units for R (0.0821 L·atm/mol·K if volume is in liters and pressure is in atmospheres).
Compare Pressures: Compare the calculated pressures for each sample. The gas sample with the highest pressure value exerts the greatest pressure.
Consider Real Gas Effects (If Necessary): If high accuracy is required, and especially if the gas is at high pressure or low temperature, consider using the van der Waals equation to account for real gas behavior. This requires knowing the van der Waals constants a and b for each gas.

Common Mistakes to Avoid

Forgetting to Convert Temperature to Kelvin: Always use Kelvin (K) for temperature in gas law calculations. K = °C + 273.15
Using Inconsistent Units: Ensure that the units for pressure, volume, and the gas constant R are consistent.
Ignoring the Number of Moles: The number of moles is a crucial factor. Don't assume that all gases exert the same pressure if the number of moles is different.
Neglecting Volume Differences: The volume of the container significantly affects the pressure.
Assuming Ideal Gas Behavior Always Applies: While often a good approximation, remember that real gases deviate from ideal behavior, especially at high pressures and low temperatures.

Real-World Applications

Understanding gas pressure is critical in many real-world applications, including:

Internal Combustion Engines: The pressure generated by the combustion of fuel-air mixtures drives the pistons in an engine.
Weather Forecasting: Atmospheric pressure is a key indicator of weather patterns.
Industrial Processes: Many chemical processes involve gases at controlled pressures.
Scuba Diving: Understanding the pressure of gases at different depths is essential for safe diving.
HVAC Systems: The pressure of refrigerants in air conditioning and refrigeration systems affects their performance.

The Impact of Altitude

It's important to remember that atmospheric pressure changes with altitude. At sea level, the standard atmospheric pressure is approximately 1 atm (101.325 kPa). As altitude increases, the atmospheric pressure decreases. Therefore, if you are comparing gas samples at 100°C at different altitudes, you need to consider the ambient atmospheric pressure. The total pressure exerted by a gas sample would be the sum of its partial pressure (calculated using the Ideal Gas Law) and the ambient atmospheric pressure.

Frequently Asked Questions (FAQ)

Q: Does the type of gas matter if the number of moles, volume, and temperature are the same?

A: According to the Ideal Gas Law, the type of gas does not matter if the number of moles, volume, and temperature are identical. However, real gases deviate slightly from ideal behavior, and these deviations are influenced by the gas's intermolecular forces and molecular size.

Q: What if the gases are mixed?

A: If the gases are mixed, you can use Dalton's Law of Partial Pressures, which states that the total pressure of a mixture of gases is equal to the sum of the partial pressures of each individual gas. The partial pressure of each gas can be calculated using the Ideal Gas Law, considering the number of moles of that specific gas in the mixture.

Q: How does humidity affect gas pressure?

A: Humidity (the amount of water vapor in the air) can affect gas pressure. Water vapor is a gas, and its presence contributes to the total pressure. The higher the humidity, the greater the partial pressure of water vapor, and consequently, the higher the total pressure.

Q: Can the Ideal Gas Law be used for liquids and solids?

A: No, the Ideal Gas Law is specifically designed for gases and is based on assumptions that do not hold true for liquids and solids (e.g., negligible intermolecular forces and particle volume).

Q: What is the difference between pressure and partial pressure?

A: Pressure refers to the force exerted by a gas per unit area. Partial pressure refers to the pressure exerted by a single gas in a mixture of gases.

Conclusion

At 100°C, the gas sample that exerts the greatest pressure is primarily determined by the number of moles of gas present and the volume it occupies. The Ideal Gas Law (PV = nRT) provides a fundamental understanding of this relationship. While real gases may deviate slightly from ideal behavior due to intermolecular forces and molecular size, the Ideal Gas Law offers a reliable approximation in most scenarios. To accurately determine which gas sample exerts the greatest pressure, carefully consider the number of moles, volume, and temperature, and apply the Ideal Gas Law accordingly. Understanding these principles is crucial in various scientific, engineering, and real-world applications where gas behavior plays a significant role. By systematically analyzing these factors, one can confidently predict and compare the pressure exerted by different gas samples under specific conditions.