Question

A gas mixture contains HBr, NO2, and C2H6 at STP.If a tiny hole is made in the container, which gas will effuse fastest?Which gas molecules have the highest average kinetic energy at this temperature?

Answer 1

Explanation:

Molar mass of HBr = 81 g/mol

Molar mass of nitrogen dioxide gas = 46 g/mol

Molar mass of ethane = 30 g/mol

Graham's Law states that the rate of effusion or diffusion of gas is inversely proportional to the square root of the molar mass of the gas. The equation given by this law follows the equation:

$\text{Rate of diffusion}\propto \frac{1}{\sqrt{\text{Molar mass of the gas}}}$

So, the gas with least molar mass will effuse out fastest from the container and that is ethane gas.

The formula for average kinetic energy is:

$K.E=\frac{3}{2}kT$

where,

k = Boltzmann’s constant = $1.38\times 10^{-23}J/K$

T = temperature = 273.15 K ( at STP)

As we can see from the formula that kinetic energy depends upon only temperature of the gas molecule.

So, from this we can say that all the gas molecules have the same average kinetic energy at this temperature.

Answer 2

If a tiny hole is made in a container with a gas mixture of HBr. NO₂ and C₂H₆ at STP, C₂H₆ will effuse fastest and they will all have the same average kinetic energy.

We have a gas mixture containinig HBr, NO₂, and C₂H₆ at STP, and a tiny hole is made in the container. The gases will experience effusion, which refers to the movement of gas particles through a small hole. According to Graham's Law, the effusion rate of a gas is inversely proportional to the square root of the mass of its particles. Considering the molar masses of HBr (80.91 g/mol), NO₂ (46.00 g/mol) and C₂H₆ (30.07 g/mol), we can predict that C₂H₆, with the lowest molar mass, will have the highest effusion rate.

On the other hand, we can calculate the average kinetic energy of a gas (KE) using the following expression.

$KE = \frac{3}{2} kT$

where,

• k: Boltzmann’s constant (1.38 × 10⁻²³ J/K)

• T: absolute temperature (standard temperature: 273.15 K)

As we can see, the average kinetic energy of a gas depends only on the temperature. For the 3 gases at STP is:

$KE = \frac{3}{2} (1.38 \times 10^{-23} J/K)(273.15K)= 5.65 \times 10^{-21} J$

If a tiny hole is made in a container with a gas mixture of HBr. NO₂ and C₂H₆ at STP, C₂H₆ will effuse fastest and they will all have the same average kinetic energy.

You can learn more about effusion here: https://brainly.com/question/3663938