Question

Consider two gases, A and B, each in a 1.0-L container with both gases at the same temperature and pressure. The mass of gas A in the container is 0.34 g and the mass of gas B in the container is 0.48 g.
A. Which gas sample has the most molecules present? B. Which gas sample has the largest average kinetic energy?C. Which gas sample has the fastest average velocity?D. How can the pressure in the 2 containers be equal to each other since the larger gas B molecules collide with the container walls more forcefully?

Answer 1

Answer:

A) the same  B) the same C) $v_{A}>v_{B}$ D) compensation between  force and velocity.

Explanation:

A) Avogadro´s law says that at the same volume, temperature and pressure two gases have the same amount of molecules.

B) Kinetic energy can be expressed like this: $E_{k} = \frac{3RT}{2N_{A} }$, where R is the ideal gas constant, T is the temperature and $N_{A}$ is the Avogadro´s number. All this values are the same in both gases thus they have the same kinetic energy.

C) Average velocity is given by the formula $v=\sqrt{\frac{3RT}{M} }$, where M is the molecular mass, if we want to know wich gas has fastest velocity is enough to know the rate between two velocities.

$\frac{V_{A} }{V_{B} } =\frac{\sqrt{\frac{3RT}{M_{A} } } }{\sqrt{\frac{3RT}{M_{B} } } } =\frac{\sqrt{M_{B} } }{\sqrt{M_{A} } } =\frac{\sqrt{\frac{m_{B} }{n} } }{\sqrt{\frac{m_{A} }{n} } } } =\frac{\sqrt{m_{B} } }{\sqrt{m_{A} } } =\frac{\sqrt{0.48g} }{\sqrt{0.34} } =1.2$, due to rate is greater than 1 $v_{A}>v_{B}$.

D) Molecules of gas B are larger, but they have a smaller velocity (collide the walls less times than gas A), by the other hand, molecules of gas A are smaller but they have a higher velocity (collide the walls with higher frequency than gas B), as a result both gases have the same kinetic energy that produces the same pressure.