Question

A mixture of 8.0 molHe and 8.0 molXe are at STP in a rigid container. Which of the following statements is TRUE? O Both gases have the same average kinetic energy O The mixture has a volume of 22.4 L O Both gases contribute equally to the density of the mixture under these conditions O Both gases have the same molecular speed O All of the above are TRUE

Answer 1

Answer : The correct option is, Both gases have the same average kinetic energy.

Explanation :

As we are given that there are 8 moles of 'He' and 'Xe'.

At STP condition,

The temperature and pressure are 273 K and 1 atm respectively.

The formula of average kinetic energy is, $K.E=\frac{3}{2}RT$. From this we conclude that the average kinetic energy is depends on the temperature only. So, at same temperature the average kinetic energy will also be same for both the gases.

As we know that the molecular speed is inversely proportional to the square root of the molecular mass. That means, it depends on the molar mass of substance. So, both the gases have the different molecular speed.

As we know that the density is directly proportional to the mass of substance. That means, it depends on the mass of substance. So, both the gases have the different density.

At STP,

As, 1 mole of He gas contains 22.4 liter volume of He gas

So, 8 mole of He gas contains $8\times 22.4=179.2$ liter volume of He gas

As, 1 mole of Xe  gas contains 22.4 liter volume of Xe gas

So, 8 mole of Xe gas contains $8\times 22.4=179.2$ liter volume of Xe gas

The mixture of has volume = 179.2 + 179.2 = 358.4 L

Hence, from the above we conclude that the correct option is, Both gases have the same average kinetic energy.