Question

the volume of hydrogen gas is twice the volume of oxygen gas. what is the mass relationship between hydrogen and oxygen gas?
the hydrogen gas is half as massive as the oxygen gas.
there is no relationship because gasses have no mass.
more information is required.
the hydrogen gas is twice as massive as the oxygen gas.

Explanation:

Step1: Recall the ideal gas law

$PV = nRT$. At the same temperature ($T$) and pressure ($P$), the amount of gas ($n$) is proportional to the volume ($V$) since $R$ is a constant. So if $V_{H_2}=2V_{O_2}$, then $n_{H_2} = 2n_{O_2}$.

Step2: Calculate the mass of each gas

The mass ($m$) of a gas is given by $m=nM$, where $M$ is the molar - mass. The molar - mass of $H_2$ is $M_{H_2}=2\ g/mol$ and the molar - mass of $O_2$ is $M_{O_2} = 32\ g/mol$. So $m_{H_2}=n_{H_2}M_{H_2}$ and $m_{O_2}=n_{O_2}M_{O_2}$. Substituting $n_{H_2} = 2n_{O_2}$ into the mass formula for $H_2$, we get $m_{H_2}=2n_{O_2}\times2\ g/mol = 4n_{O_2}\ g/mol$, and $m_{O_2}=n_{O_2}\times32\ g/mol$.

Step3: Find the mass ratio

The ratio of the mass of $H_2$ to the mass of $O_2$ is $\frac{m_{H_2}}{m_{O_2}}=\frac{4n_{O_2}}{32n_{O_2}}=\frac{1}{8}$. So the hydrogen gas is $\frac{1}{8}$ as massive as the oxygen gas, which means more information (such as temperature and pressure conditions to be more precise in a non - standard situation) is required to accurately state the mass relationship in a general sense.

Answer:

More information is required.