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Gas Laws - Equations and Formulas

The Organic Chemistry Tutor・2 minutes read

Pressure, volume, moles, gas constant, and temperature play significant roles in gas laws, with equations like Boyle's, Charles's, and Avogadro's law explaining various gas behaviors. Mole fraction calculations, Dalton's law, and root mean square velocity equations provide insights into gas mixtures, total pressure, and gas velocity based on molar mass and temperature.

Insights

  • Pressure, volume, moles, gas constant, and temperature are crucial components of the ideal gas law equation (PV = nRT), with specific units required for each parameter to ensure accurate calculations.
  • Gas laws such as Boyle's, Charles's, and Gay-Lussac's laws explain the relationships between pressure, volume, temperature, and moles in gases, offering insights into phenomena like gas expansion in balloons and pressure changes in non-expandable containers.

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Recent questions

  • How is gas density at STP calculated?

    By dividing molar mass by 22.4.

  • What is Dalton's law of partial pressures?

    Total pressure equals sum of partial pressures.

  • How does Graham's law of effusion work?

    Rate inversely related to square root of molar mass.

  • What is the ideal gas law equation?

    PV = nRT, involving pressure, volume, moles, gas constant, and temperature.

  • How are mole fractions calculated in gas mixtures?

    By dividing moles of specific gas by total moles.

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Summary

00:00

Gas Laws and Pressure Conversions Explained

  • Pressure is defined as force divided by area, with one pascal equal to one newton per square meter.
  • In chemistry, units of pressure are often expressed in atm, with 1 atm equal to 760 torr or 101.3 kilopascals.
  • The ideal gas law equation, PV = nRT, involves pressure, volume, moles, gas constant (0.08206), and temperature in Kelvin.
  • To use the ideal gas law equation, ensure pressure is in atm, volume in liters, and temperature in Kelvin.
  • To convert temperature to Kelvin, add 273 to Celsius temperature; Fahrenheit to Celsius conversion is F = 1.8C + 32.
  • Boyle's law describes the inverse relationship between pressure and volume, with P1V1 = P2V2.
  • Charles's law shows the direct linear relationship between volume and temperature, with V1/T1 = V2/T2.
  • Gay-Lussac's law relates pressure and temperature, with P1/T1 = P2/T2, showing a proportional increase in pressure with temperature.
  • Combining Boyle's, Charles's, and Gay-Lussac's laws can explain scenarios like gas expansion in a balloon due to increased temperature.
  • Avogadro's law links moles and volume, with V1/n1 = V2/n2, indicating that increasing moles of gas leads to volume expansion.

19:20

Gas Expansion and Density Relationships

  • Gas volume increases as gas expands due to reduced pressure
  • Pressure fluctuations lead to constant pressure at the end of the system change
  • Increasing gas moles results in gas volume expansion
  • In a non-expandable container, increasing moles raises pressure without volume change
  • For a balloon, adding gas moles increases volume, following Avogadro's law
  • STP (Standard Temperature and Pressure) values: 273 K, 1 atm, 22.4 L for one mole of gas
  • Derivation of gas density equation: density = mass/volume
  • Molar mass calculation: mass/moles, useful for identifying gases
  • Gas density equation: pressure x molar mass = density x R x T
  • Relationship between pressure, molar mass, volume, and temperature on gas density

37:30

Gas Mixtures: Mole Fractions and Pressures Explained

  • Mole fraction represents the proportion of a specific gas in a mixture, calculated by dividing the moles of that gas by the total moles.
  • For example, in a mixture with 10 total moles, a mole fraction of 0.2 for argon means 20% of the molecules are argon.
  • The mole fraction of oxygen (O2) in the same mixture is 0.1, indicating 10% of the molecules are oxygen.
  • The sum of all mole fractions in a mixture always equals 1, representing 100% of the total.
  • Dalton's law states that the total pressure of a gas mixture is the sum of the partial pressures of each gas.
  • Partial pressure is calculated by multiplying the mole fraction of a gas by the total pressure.
  • The root mean square velocity of a gas is derived from the average kinetic energy equation, proportional only to temperature.
  • The root mean square velocity equation includes the gas constant R as 8.3145 J/mol*K, with temperature in Kelvin and molar mass in kilograms.
  • Increasing temperature raises gas velocity, while increasing molar mass lowers velocity due to the square root relationship.
  • Graham's law of effusion connects the rates of effusion of two gases to their molar masses, with the ratio of velocities being the square root of the molar mass ratio.

56:05

Graham's Law and Gas Density Calculation

  • Graham's law of effusion states that the rate of effusion is inversely related to the square root of the molar mass of a gas, with the formula r2/r1 = √(m1/m2). As the molar mass of a gas increases, its velocity decreases, leading to a decrease in the rate of effusion. For example, comparing hydrogen gas (molar mass of 2) to oxygen gas (molar mass of 32), the rate of effusion for oxygen would be 25 if the rate for hydrogen is 100, due to the square root relationship between molar mass and rate of effusion.
  • Gas density at STP (standard temperature and pressure) can be calculated using the formula density = molar mass / 22.4, where one mole of gas occupies 22.4 liters at STP. This equation allows for the determination of gas density in grams per liter, with the molar mass of a gas being equal to density multiplied by 22.4 only at STP.
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