Question

Two identical 732.0 L tanks each contain 212.0 g of gas at 293 K, with neon in one tank and nitrogen in the other. Based on the assumptions of kinetic-molecular theory, rank the gases from low to high for each of the following properties: a) average speed; b) pressure; c) collision frequency; d) density (g/L)

Answer 1

Explanation:

The given data is as follows.

           V = 732.0 L,     m = 212.0 g,     T = 293 K

It is known that molar mass of nitrogen is 28.02 g/mol and molar mass of neon is 20.18 g/mol.

(a)   As it is given that mass of both the gases is same. Therefore, higher is the molar mass of the gas, slower will be its average speed.

Therefore, average speed of nitrogen is less that the average speed of neon.

(b)   According to the ideal gas equation, PV = nRT.

So, first calculate the number of moles of nitrogen are as follows.

               n = $\frac{mass}{\text{molar mass}}$

                  = $\frac{212 g}{28.02 g/mol}$

                  = 7.56 mol

Now, pressure of nitrogen will be as follows.

             PV = nRT

$P \times 732.0 L = 7.56 mol \times 0.0821 L atm/mol K \times 293 K$

          P = 0.248 atm

Whereas moles of neon will be as follows.

            n = $\frac{mass}{\text{molar mass}}$

                  = $\frac{212 g}{20.18 g/mol}$

                  = 10.5 mol

Now, pressure of neon will be as follows.

             PV = nRT

$P \times 732.0 L = 10.5 mol \times 0.0821 L atm/mol K \times 293 K$

          P = 0.345 atm

Therefore, pressure of neon is more than the pressure of nitrogen gas.

(c)   Formula for collision frequency is as follows.

              f = $\frac{\nu}{\lambda}$

As    $\nu_{rms} = \sqrt{\frac{3RT}{M}}$

where,     M = molar mass of gas

Therefore, collision frequency is inversely proportional to molar mass of a gas. And, as nitrogen has high molar mass than neon.

Therefore, collision frequency of nitrogen is less than that of neon.

(d)   As density is mass divided by volume.

Mathematically,    Density = $\frac{mass}{volume}$

Also, in the given situation mass and volume for both the gases is same. Hence, density of both nitrogen and neon will be the same at given temperature.