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Ideal Gases (DP IB Chemistry)

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    What assumptions are made in the kinetic theory of gases?

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  • What assumptions are made in the kinetic theory of gases?

    The assumptions made in the kinetic theory of gases are:

    • The gas molecules are moving very fast and randomly

    • The molecules hardly have any volume

    • The gas molecules do not attract or repel each other (no intermolecular forces)

    • No kinetic energy is lost when the gas molecules collide with each other (elastic collisions)

    • The temperature of the gas is directly proportional to the average kinetic energy of the molecules

  • True or False?

    Ideal gas molecules have significant volume.

    False.

    Ideal gas molecules are assumed to have negligible volume.

  • Define elastic collision.

    An elastic collision is when no kinetic energy is lost when gas molecules collide with each other.

  • What is the relationship between temperature and average kinetic energy of gas molecules?

    The temperature of the gas is directly proportional to the average kinetic energy of the molecules, i.e. as temperature increases, the average kinetic energy increases.

  • What is an ideal gas?

    An ideal gas is a gas that follows the kinetic theory of gases.

  • True or False?

    Real gases exactly fit the description of ideal gases.

    False.

    Real gases do not exactly fit the description of ideal gases but may come very close.

  • What factors does the volume of a gas depend on?

    The volume that a gas occupies depends on its pressure and temperature.

  • What is the difference between elastic and inelastic collisions?

    In an elastic collision, energy is conserved and particles move away in opposite directions.

    In an inelastic collision, kinetic energy is not conserved and particles usually stick together

  • True or False?

    The kinetic theory assumes gas molecules attract each other.

    False.

    The kinetic theory assumes gas molecules do not attract or repel each other (no intermolecular forces).

  • How do gases exert pressure in a container?

    Gases exert pressure as the gas molecules are constantly colliding with the walls of the container.

  • State Boyle's Law.

    Boyle's Law states that pressure is inversely proportional to volume at constant temperature.

  • What is the mathematical expression of Boyle's Law?

    The mathematical expression of Boyle's Law is P ∝ 1/V or PV = constant.

  • True or False?

    Decreasing the volume of a gas at constant temperature increases its pressure.

    True.

    Decreasing the volume of a gas at constant temperature increases its pressure.

  • Define Charles' Law.

    Charles' Law states that volume is directly proportional to temperature in Kelvin at constant pressure.

  • What is the mathematical expression of Charles' Law?

    The mathematical expression of Charles' Law is V ∝ T or V/T = constant.

  • How does increasing temperature affect gas pressure at constant volume?

    Increasing temperature at constant volume increases the pressure of the gas.

  • True or False?

    Pressure is inversely proportional to temperature at constant volume.

    False.

    Pressure is directly proportional to temperature at constant volume.

  • State the ideal gas equation.

    The ideal gas equation is PV = nRT.

  • What does P represent in the ideal gas equation?

    P represents pressure (in pascals, Pa) in the ideal gas equation.

  • What does V represent in the ideal gas equation?

    V represents volume (in m³) in the ideal gas equation.

  • What does n represent in the ideal gas equation?

    n represents the number of moles of gas (mol) in the ideal gas equation.

  • What does R represent in the ideal gas equation?

    R represents the gas constant (8.31 J K⁻¹ mol⁻¹) in the ideal gas equation.

  • What does T represent in the ideal gas equation?

    T represents temperature (in Kelvin, K) in the ideal gas equation.

  • True or False?

    The ideal gas equation can be used to calculate the molar mass of a gas.

    True.

    The ideal gas equation can be used to calculate the molar mass of a gas.

  • How do you convert temperature from Celsius to Kelvin?

    To convert temperature from Celsius to Kelvin, add 273 to the Celsius temperature.

  • How do you convert pressure from kilopascals to pascals?

    To convert pressure from kilopascals to pascals, multiply by 1000.

  • How do you convert volume from dm3 to m3?

    To convert volume from dm3 to m3, divide by 1000.

  • How do you convert volume from cm3 to m3?

    To convert volume from dm3 to m3, divide by 1000000.

  • True or False?

    Pressure in the ideal gas equation should be in pascals (Pa).

    True.

    Pressure in the ideal gas equation should be in pascals (Pa).

  • Calculate the volume, in dm3, occupied by 0.5 mol of oxygen at a pressure of 220 kPa and a temperature of 21 °C.

    The volume is 5.55 dm3.

    • P = 220 kPa = 220 000 Pa

    • n = 0.5 mol

    • R = 8.31 J K-1 mol-1

    • T = 21 oC = 294 K

    • V = fraction numerator n R T over denominator P end fraction = fraction numerator 0.5 cross times 8.31 cross times 294 over denominator 220 space 000 end fraction = 0.00555 = 5.55 dm3

  • Calculate the pressure of a gas, in kPa, given that 0.10 moles of the gas occupy 10.0 dm3 at a temperature of 25 oC.

    The pressure is 24.5 kPa.

    • n = 0.10 mol

    • V = 10.0 dm3 = 0.0100 m3 = 10.0 x 10-3 m3 

    • R = 8.31 J K-1 mol-1

    • T = 25 oC = 298 K

    • P = fraction numerator n R T over denominator V end fraction = fraction numerator 0.10 cross times 8.31 cross times 298 over denominator 10.1 cross times 10 to the power of negative 3 end exponent end fraction = 24 519 Pa = 24.5 kPa

  • Calculate the temperature of a gas, in oC, if 0.05 moles of the gas occupy 1.0 dm3 at a pressure of 100 kPa.

    The remperature is -32.3 oC.

    • n = 0.05 mol

    • V = 1.0 dm3 = 0.001 m3 = 1.0 x 10-3 m3 

    • R = 8.31 J K-1 mol-1

    • P = 100 kPa = 100 000 Pa

    • T = fraction numerator P V over denominator n R end fraction = fraction numerator 100 space 000 cross times 1.0 cross times 10 to the power of negative 3 end exponent over denominator 0.05 cross times 8.31 end fraction = 240.67 K = -32.3 oC

  • A flask of volume 1000 cm3 contains 6.0 g of a gas. The pressure in the flask was 300 kPa and the temperature was 23 °C.

    Calculate the molar mass of the gas.

    The molar mass of the gas is 54.2 g mol-1.

    • P = 300 kPa = 300 000 Pa

    • V = 1000 cm3 = 0.001 m3 = 1.0 x 10-3 m3 

    • R = 8.31 J K-1 mol-1

    • T = 23 oC = 296 K

    • n = fraction numerator P V over denominator R T end fraction = fraction numerator 300 space 000 cross times 1.0 cross times 10 to the power of negative 3 end exponent over denominator 8.31 cross times 296 end fraction = 0.12 mol

    • M = fraction numerator 6.5 over denominator 0.12 end fraction = 54.2 g mol-1

  • Under what conditions do real gases show significant deviation from the ideal gas equation?

    Real gases show significant deviation from the ideal gas equation when the temperature is very low or the pressure is very high.

  • What is a key assumption of the kinetic theory about gas molecule volume?

    The kinetic theory assumes that the volume the actual gas molecules themselves take up is tiny compared to the volume the gas occupies in a container.

  • True or False?

    The kinetic theory assumes no interaction between gas molecules.

    True.

    The kinetic theory assumes that when gas molecules are far apart there is very little interaction between the molecules.

  • How do intermolecular forces affect gas pressure at high pressures?

    At high pressures, intermolecular forces cause attraction between molecules, reducing the number of collisions with the container walls and resulting in less pressure than expected by the ideal gas equation.

  • What happens to the fraction of space occupied by gas molecules at low temperatures and high pressures?

    At low temperatures and high pressures, the fraction of space taken up by the molecules becomes substantial compared to the total volume.

  • True or False?

    Real gases always behave exactly like ideal gases.

    False.

    Real gases deviate from ideal gas behavior, especially at low temperatures and high pressures.

  • How does the volume of gas molecules affect the accuracy of the ideal gas equation?

    The ideal gas equation becomes increasingly inaccurate at low temperatures and high pressures because the volume of gas molecules becomes significant compared to the total volume.

  • What causes the pressure of real gases to be less than expected by the ideal gas equation at high pressures?

    At high pressures, intermolecular attractions reduce collisions with container walls, causing the pressure to be less than expected by the ideal gas equation.

  • True or False?

    The ideal gas equation is always accurate for all gases under all conditions.

    False.

    The ideal gas equation shows significant deviations for real gases, especially at low temperatures and high pressures.

  • How do low temperatures affect the behavior of real gases compared to ideal gases?

    At low temperatures, real gases deviate significantly from ideal gas behavior because the gas molecules are closer together, making intermolecular forces more significant.

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