Grade 10 SCIENCE | Quarter 4 Module 2 | Kinetic Molecular Theory, Avogadro's Law and Ideal Gas Law

The kinetic molecular theory of gases helps understand the properties of gases at a molecular level, especially since gases are invisible. This theory has several key assumptions or postulates to explain gas behavior.

The first assumption is that gases are composed of molecules with distances far greater than their dimensions. The second states that gas molecules are in constant random motion, frequently colliding with perfectly elastic collisions, meaning no loss of kinetic energy. The third assumption is that attractive and repulsive forces between gas particles are considered insignificant due to their weakness. The fourth, already discussed, highlights that the average kinetic energy of gas molecules is directly related to its temperature: faster movement means higher temperature, and slower movement means lower temperature.

Avogadro's Law, named after Amedeo Avogadro, relates the number of moles (n) and volume (V) of a gas, stating they are directly related. This means as one quantity increases, the other also increases, provided pressure and temperature are held constant. Mathematically, it's expressed as V1/n1 = V2/n2, where V1 and V2 are initial and final volumes, and n1 and n2 are initial and final amounts of gas in moles.

A problem is presented: a 1.2-liter gas sample contains 0.07 mole of nitrogen. The question asks for the amount of gas in a 20-liter sample at the same temperature and pressure. The knowns are V1 (1.2 L), n1 (0.07 mole), and V2 (20 L), with n2 being the unknown. By substituting these values into Avogadro's formula and solving, n2 is calculated to be approximately 1.17 moles, demonstrating the direct relationship between volume and moles.

Another problem involves 47.6 moles of nitrogen gas occupying 3.80 liters at 25 degrees Celsius, asking what volume it will occupy at 73 moles. Here, n1 (47.6 moles), V1 (3.80 liters), and n2 (73 moles) are given, with V2 being the unknown. Temperature is noted as constant. Solving with Avogadro's formula, V2 is found to be approximately 5.83 liters, confirming that an increase in moles leads to an increase in volume.

The Ideal Gas Law, pioneered by Benoit Paul Émile Clapeyron, combines Boyle's Law (volume inversely proportional to pressure), Charles' Law (volume directly proportional to temperature), and Avogadro's Law (volume directly proportional to the amount of substance). By combining these relationships, the ideal gas law equation PV = nRT is derived, where R is the universal gas law constant.

For the Ideal Gas Law, strict unit adherence is necessary: pressure (P) must be in atmospheres, volume (V) in liters, amount of substance (n) in moles, and temperature (T) in Kelvin. The universal gas constant (R) is 0.0821 liter·atmosphere/(mole·Kelvin), and its units serve as a guide for the required units of the other variables in the equation.

The first problem requires finding the number of moles (n) of an ideal gas based on given volume (6.5 liters), pressure (2.9 atmospheres), and temperature (27 degrees Celsius). The temperature is first converted to Kelvin (300.15 K). Substituting these values into PV=nRT and solving for n, the amount of gas is approximately 0.76 moles.

The second problem asks for the temperature (T) at which 0.654 moles of neon gas (n) will occupy 15.2 liters (V) at 1.95 atmospheres (P). Given n, V, P, and the constant R, the values are plugged into the PV=nRT equation. Solving for T, the temperature is found to be 552 Kelvin.