Physics Chapter on Gas Laws
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Questions and Answers

What does the equation $P = rac{2}{3} rac{KE}{V}$ represent?

  • The kinetic energy of a gas is equal to two-thirds of its pressure per unit volume.
  • The volume of gas is directly proportional to its pressure and kinetic energy.
  • The pressure of a gas is equal to one-third of its kinetic energy per unit volume.
  • The pressure of a gas is equal to two-thirds of its kinetic energy per unit volume. (correct)

    • Which equation correctly relates pressure and average kinetic energy?

  • P = m ar{c^2}
  • P = n m ar{c^2}
  • P_{ ext{avg}} = 3n m ar{c^2}
  • P = rac{1}{3}m ar{c^2} (correct)

    • How is average kinetic energy $ar{c^2}$ calculated?

  • $ar{c^2} = rac{n}{c_1^2 + c_2^2 + ext{...} + c_n^2}$
  • $ar{c^2} = rac{1}{n}(c_1 + c_2 + ... + c_n)$
  • $ar{c^2} = rac{c_1^2 + c_2^2 + ext{...} + c_n^2}{n}$ (correct)
  • $ar{c^2} = c_1 + c_2 + rac{c_n}{n}$

    • What does the variable M stand for in the equations?

    <p>The total mass of the gas.</p> Signup and view all the answers

    What is the relationship between pressure (P) and velocity (c) derived from the equations?

    <p>c = rac{3P}{m}</p> Signup and view all the answers

    What does Graham's law of diffusion state about the relationship between the rate of diffusion and the density of gases?

    <p>They are inversely proportional.</p> Signup and view all the answers

    In the equation $\frac{R_1}{R_2} = \sqrt{\frac{d_2}{d_1}}$, what does $R_1$ represent?

    <p>Rate of diffusion of gas 1</p> Signup and view all the answers

    Which of the following gases would diffuse the slowest according to Graham's law?

    <p>A heavier gas with high density</p> Signup and view all the answers

    What can be concluded about a lighter gas based on Graham's law of diffusion?

    <p>It diffuses more quickly than heavier gases.</p> Signup and view all the answers

    If the density of gas 1 is greater than that of gas 2, which statement is true according to Graham's law?

    <p>Gas 2 will diffuse faster than gas 1.</p> Signup and view all the answers

    Study Notes

    Graham's Law of Diffusion

    • The rate of diffusion of a gas is inversely proportional to the square root of its density.
    • This means that lighter gases diffuse faster than heavier gases.
    • The equation for Graham's law is: $\frac{R_1}{R_2} = \sqrt{\frac{d_2}{d_1}}$

    Gas Pressure and Kinetic Energy

    • The pressure of a gas is proportional to its kinetic energy per unit volume.
    • The equation for pressure is: $P = \frac{1}{3} \frac{M}{V} c^2$
    • The pressure is equal to two-thirds of the kinetic energy per unit volume: $P = \frac{2}{3}\frac{KE}{V}$

    Force acting on molecules due to wall

    • The force exerted by a gas molecule on a wall is a result of the molecule's momentum change during a collision.
    • The pressure of the gas is related to the average kinetic energy of the molecules.

    Gay-Lussac's Law of Pressure

    • The pressure of a gas is directly proportional to its absolute temperature when the volume is constant.
    • The equation for Gay-Lussac's law is: $\frac{P_2}{T_2} = \frac{P_1}{T_1}$

    Pressure Coefficient

    • The pressure coefficient of a gas at constant volume is the change in pressure per unit degree centigrade rise in temperature.

    Dalton's Law of Partial Pressures

    • The total pressure of a mixture of gases is equal to the sum of the partial pressures of the individual gases.
    • The equation for Dalton's law is: $P = P_1 + P_2 +...$

    Gas Pressure Calculation

    • The pressure exerted by a gas is related to the frequency of collisions of gas molecules with the container walls and their momentum change during collisions.

    Avogadro's Law

    • Equal volumes of all gases under the same conditions of temperature and pressure contain the same number of molecules.
    • This is represented mathematically as: $PV = \frac{m}{M}RT$
    • Avogadro's number is $6.023 \times 10^{23}$.

    Gas Laws

    • Boyle's Law: PV = constant, where pressure is inversely proportional to volume.
    • Charles' Law: V/T = constant, where volume is directly proportional to temperature.
    • Volume coefficient: The change in volume per degree rise in temperature at constant pressure.

    Ideal Gas vs. Real Gas

    • Ideal gas equation: $PV = nRT$
    • Specific gas constant (r): $r = \frac{R}{M}$
    • Real gases deviate from ideal behavior at high pressure and low temperatures.
    • Vander Waals equation: $P + \frac{a}{V^2}(V-b) = RT$

    Chapter 9: Behaviour of Perfect Gas and Kinetic Theory

    • Ideal Gas: An ideal gas has zero molecular size and zero intermolecular forces. This state is attainable at low pressure and high temperature.
    • Ideal Gas Equation: $\frac{V_1}{T_1} = \frac{V_2}{T_2}$
    • Universal Gas Constant (R): It is constant for all gases and its value can be determined as $R = \frac{P_o V_o}{T_o}$
    • Note: Normal Pressure = $P_o = 0.76 \times 13600 \times 9.8$ N/m⁻² and $V_o = 22.4 \ L = 0.0224 \ m^3$

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    Description

    Test your understanding of key gas laws including Graham's Law of Diffusion, Gay-Lussac's Law of Pressure, and the relationship between gas pressure and kinetic energy. This quiz covers essential equations and principles that govern gas behavior and molecular interactions. Perfect for students looking to reinforce their knowledge in physics.

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