Answer
a. the mass of gas in container A is equal to the mass of gas in container B.
b. the density of gas in container A is two times grater than the density of gas in container B.
c. If the volume of container A were increased to the same volume as container B, the density of gas in container A would be the same with the density of gas in container B.
Work Step by Step
a. In picture it is given the same number of gas atoms in container A and container B. Since it is the same gas in both containers, and the number of atoms is the same, the mass of gas in container A is equal to the mass of gas in container B.
$m_{A}$ = $m_{B}$ = m
b. Container A has the greater density of gas.
d = $\frac{m}{V}$
We can write the formula for density of gas in container A :
$d_{A}$ = $\frac{m}{V_{A}}$
We can write the formula for density of gas in container B :
$d_{A}$ = $\frac{m}{V_{B}}$
We know that ${V_{A}}$ = $\frac{1}{2}$ x ${V_{B}}$, so
$d_{A}$ = $\frac{m}{\frac{1}{2}{V}_{B}}$
$d_{A}$ = 2 $\frac{m}{V_{B}}$
$d_{A}$ =2 $d_{B}$
So the density of gas in container A is two times grater than the density of gas in container B.
c. If the volume of container A were increased to the same volume as container B, the density of gas in container A would be the same with the density of gas in container B.
From formulas above:
$d_{A}$ = $\frac{m}{V_{A}}$
$d_{B}$ = $\frac{m}{V_{B}}$
As ${V_{A}}$ =${V_{B}}$ , than: $d_{A}$ = $d_{B}$
