Which of the following statements is(are) true? For the false statements, correct them. a. At constant temperature, the lighter the gas molecules, the faster the average velocity of the gas molecules. b. At constant temperature, the heavier the gas molecules, the larger the average kinetic energy of the gas molecules. c. A real gas behaves most ideally when the container volume is relatively large and the gas molecules are moving relatively quickly. d. As temperature increases, the effect of interparticle interactions on gas behavior is increased. e. At constant V and T, as gas molecules are added into a container, the number of collisions per unit area increases resulting in a higher pressure. f. The kinetic molecular theory predicts that pressure is inversely proportional to temperature at constant volume and moles of gas.

Interpretation For the following statements, true statements should be found and for the false statements it should be corrected.

Concept introduction:

• Kinetic molecular theory explains the properties of ideal gas. From the postulates of kinetic molecular theory it is clear that kinetic energy of gas particle is directly proportional to the Kelvin temperature of the gas.

    Average kinetic energy of gas can be determined as,  KEavg= (3/2)RT

• The average  velocity can be determined,

                                                         μave= (8 R T π M)1/2 (1)

        R =8.314 JK molM= Molar mass in  kg

• Ideal gas law tends to hold best at low pressure and high temperature

  A modified ideal gas equation on account of molecular size and molecular interaction forces is termed as Van der Waals equation.

        That is,                [P+a(nV)2](V-nb) = nRT

‘a’ and ‘b’ is called Van der Waals coefficient and are characteristic of the   individual gas

Where,

          P = pressure in atmospheres

          V= volumes in liters

          n = number of moles

          R =universal gas constant ( 0.08206L×atm/K×mol )

          T = temperature in kelvins

• At constant temperature and volume, the number of collision pre unit area increases by increasing the number of moles per unit area.

Explanation

At constant temperature, the lighter gas molecules, the faster the average velocity of the gas molecules.

The average velocity can be determined,

                                                         μave= (8 R T π M)1/2

From the given equation it is clear that average velocity of a gas is inversely proportional to the molar mass. So, at constant temperature, the lighter gas molecules, the faster the average velocity of the gas molecules

A real gas behaves most ideally when the container volume is relatively large and the gas molecules are moving relatively quickly.

As the container volume is relatively large, the pressure inside the container must be low. Ideal gas law tends to hold best at low pressure and high temperature.

It can be clearly explained as follows,

A modified ideal gas equation on account of molecular size and molecular interaction forces is termed as Van der Waals equation.

Van der Waals equation is

                [P+a(nV)2](V-nb) = nRT

At low pressure and high temperature the molar volume of a gas will be relatively large and actual volume of the gas ‘nb ’is very smaller than the molar volume(V)

So, these two terms can be neglected and Vander Waals equation becomes,

P V=n RT

At constant V and T, as gas molecules are added into a container the number of collision per unit area increases resulting in a higher pressure

At constant temperature and volume, the number of collision pre unit area increases by increasing the number of moles per unit area

So, the given statement, at constant V and T, as gas molecules are added into a container the number of collision per unit area increases resulting in a higher pressure is true.

Corrected false statement

Given false statement:

At constant temperature, the heavier the gas molecules, and the larger the average kinetic energy of the gas molecules

True statement:

At constant temperature, the average kinetic energy of a gas will be constant.

Kinetic molecular theory explains the properties of ideal gas