Question

Two flexible containers for gases are at the same tem­perature and pressure. One holds 0.50 gram of hy­drogen and the other holds 8.0 grams of oxy­gen. Which of the following statements re­garding these gas samples is FALSE? The volume of the hydrogen container is the same as the volume of the oxygen container.
A The number of molecules in the hydrogen con­tainer is the same as the number of molecules in the oxygen container.
B The density of the hydrogen sample is less than that of the oxygen sample.
C The average kinetic energy of the hydrogen molecules is the same as the average kinetic en­ergy of the oxygen molecules.
D The average speed of the hydrogen molecules is the same as the average speed of the oxygen molecules.

Answer 1

Answer: A The number of molecules in the hydrogen con­tainer is the same as the number of molecules in the oxygen container.

D The average speed of the hydrogen molecules is the same as the average speed of the oxygen molecules.

Explanation:

A. According to avogadro's law, 1 mole of every substance occupies 22.4 L at NTP, weighs equal to the molecular mass and contains avogadro's number $6.023\times 10^{23}$ of particles.

$\text{Number of moles}=\frac{\text{Given mass}}{\text{Molar mass}}$

$\text{Number of moles of hydrogen}=\frac{0.50g}{2g/mol}=0.25moles$

$\text{Number of moles of oxygen}=\frac{8.0g}{16g/mol}=0.5moles$

Thus oxygen will have more molecules as it has more moles.

B. Density is defined as the mass contained per unit volume.

$Density=\frac{mass}{Volume}$

As volume is same, density depends on mass. As mass of hydrogen is less, its density will also be less.

C. Average kinetic energy is defined as the average of the kinetic energies of all the particles present in a system. It is determined by the equation:

$K=\frac{3RT}{2}$

Thus at same temperature, the average kinetic energy of the hydrogen molecules is the same as the average kinetic en­ergy of the oxygen molecules.

D. The formula for average speed is  :

$\nu_{av}=\sqrt{\frac{8RT}{\pi M}}$

Thus as molecular mass of hydrogen is less than that of oxygen , the average speed of hydrogen will be more than that of oxygen.