Understanding the Total Pressure in a Flask Containing Hydrogen and Oxygen Gases
Understanding the Total Pressure in a Flask Containing Hydrogen and Oxygen Gases
Consider a flask that contains three times as many moles of hydrogen (H2) gas as it does of oxygen (O2) gas. If hydrogen and oxygen are the only gases present, this article will explain how to determine the total pressure in the flask if the partial pressure due to oxygen is p.
Conceptual Framework: The Ideal Gas Law
The Ideal Gas Law, described by the equation PV nRT, provides a foundation for understanding the behavior of gases in a container. Under the assumption that both gases in the flask can be modeled as ideal gases, the volume of a mole of gas is fixed at a given temperature and pressure. At standard temperature and pressure (STP: T 293 K, p 1 atm), one mole of an ideal gas occupies approximately 22.4 liters (or cubic decimeters).
Given this background, we'll explore how to calculate the total pressure in the flask based on the partial pressures of hydrogen and oxygen.
Total Pressure Calculation
Let's denote the partial pressure due to oxygen as p. According to the problem, the flask contains three times as many moles of hydrogen gas as it does of oxygen gas. Therefore, if the partial pressure due to oxygen is p, the partial pressure due to hydrogen (H2) must be three times that, or 3p.
To find the total pressure, we sum the partial pressures of the two gases:
Total Pressure Partial Pressure of Hydrogen Partial Pressure of Oxygen
Total Pressure 3p p
Total Pressure 4p
This shows that the total pressure in the flask is four times the partial pressure of the oxygen gas.
The Importance of Ideal Gas Assumptions
For gases to be considered ideal, they must follow the Ideal Gas Law under certain conditions. While real gases may deviate from these conditions, for all practical purposes, the assumption of ideal gas behavior provides a useful approximation. The key assumptions are:
Particles have negligible volume. Individual molecules occupy only a small volume, and their contribution to the total container volume is negligible. Intermolecular forces are negligible. There are no significant attractive or repulsive forces between the gas molecules. Collisions are perfectly elastic. When gas molecules collide, the total kinetic energy is conserved. Average kinetic energy is proportional to the absolute temperature. The thermal energy of the gas particles is directly related to the temperature of the gas.Given these assumptions, the total pressure in the flask can be accurately calculated using partial pressures.
Conclusion
The total pressure in the flask containing three times as many moles of hydrogen gas as oxygen gas is four times the partial pressure of the oxygen gas. This result is derived using the principles of the Ideal Gas Law and the concept of partial pressures. By understanding these principles, we can accurately predict the behavior of gases in various scenarios.