Ideal Gas Law Flashcards

Avogadro's Law

• For a given mass of gas, the volume (V) is directly proportional to the number of moles (n) if temperature and pressure are constant. This relationship holds true under conditions where the gas behaves ideally, meaning there are minimal intermolecular forces and the gas particles occupy negligible volume compared to the total volume.

• V \propto n

• One mole of any ideal gas has a volume of approximately 24 dm^3 at standard room temperature (20^oC or 293.15 K) and pressure (1 atm). This molar volume is a useful benchmark for estimating gas quantities in laboratory settings.

• \frac{V1}{n1} = \frac{V2}{n2}

  • V_1 = initial volume

  • n_1 = initial number of moles of gas

  • V_2 = final volume

  • n_2 = final number of moles of gas

Boyle's Law

• For a fixed amount of gas (i.e., constant number of moles) at constant temperature, the pressure (P) exerted by the gas is inversely proportional to its volume (V). This law is applicable in scenarios where the gas is compressed or expanded slowly, allowing the temperature to remain constant.

• P \propto \frac{1}{V}, where P is pressure and V is volume.

• P1V1 = P2V2

Charles's Law

• The volume (V) of a gas is directly proportional to its absolute temperature (T) when the pressure is held constant. The temperature must be expressed in Kelvin because the Kelvin scale starts from absolute zero, which is essential for direct proportionality.

• V \propto T, where V is volume and T is temperature in Kelvin.

• \frac{V1}{T1} = \frac{V2}{T2}

• Temperature in Kelvin = 273.15 + temperature in ^oC

Ideal Gas Law

• PV = nRT

  • P = pressure (Pa)

  • V = volume (m^3)

  • n = number of moles

  • T = temperature (Kelvin)

  • R = Gas law constant (8.314 \frac{m^3 \cdot Pa}{K \cdot mol})

• The ideal gas law combines Boyle's, Charles's, and Avogadro's laws and is used to describe the state of an ideal gas. It assumes that gas particles have no volume and no intermolecular forces, which is a good approximation for real gases at low pressures and high temperatures.

• Assumptions for Ideal Gases:

  • Particles are in constant, random motion, colliding with the walls of the container. This motion is due to the thermal energy of the gas.

  • The combined volume of the particles is negligible compared to the total volume of the gas. This assumption is valid when the gas is at low pressure.

  • Particles exert no attractive or repulsive forces on one another. This means that the gas is considered non-interactive, which is more likely at high temperatures.

  • Collisions between particles are perfectly elastic, meaning no kinetic energy is lost during collisions.

  • Average kinetic energy of the particles is directly proportional to the absolute temperature in Kelvins. As temperature increases, the particles move faster, increasing the pressure if the volume is constant.

R Constant Values:

• 8.3144598 \frac{J}{K \cdot mol}

• 8.3144598 \times 10^3 \frac{amu \cdot m^2}{s^2 \cdot K}

• 8.3144598 \times 10^{-2} \frac{L \cdot bar}{K \cdot mol}

• 8.3144598 \frac{m^3 \cdot Pa}{K \cdot mol}

• 62.363577 \frac{L \cdot Torr}{K \cdot mol}

• 1.9872036 \times 10^{-3} \frac{kcal}{K \cdot mol}

• $$8.2057338 \times 10^{-5} \frac{m^3 \

The key concepts covered in the provided notes include Avogadro's Law, Boyle's Law, Charles's Law, and the Ideal Gas Law. These laws describe the relationships between pressure, volume, temperature, and the number of moles for ideal gases, along with the conditions under which these laws are applicable.