Question

use the following information to answer the next two questions

1. the ratio of the numbers of co₂(g) moles to no(g) moles is
2. the gas samples in the above containers have:

Explanation:

Step1: Recall the ideal - gas law

The ideal - gas law is $PV = nRT$, where $P$ is pressure, $V$ is volume, $n$ is the number of moles, $R$ is the ideal - gas constant, and $T$ is temperature. For the two gases, assume the volume of the containers is the same ($V_{CO_2}=V_{NO}$), the pressure is the same ($P_{CO_2}=P_{NO} = 101.3\ kPa$), and the temperature is the same ($T_{CO_2}=T_{NO}=273\ K$). From $PV = nRT$, we can solve for $n$: $n=\frac{PV}{RT}$. Since $P$, $V$, $R$, and $T$ are the same for both gases, the number of moles of $CO_2$ and $NO$ is the same. So the ratio of the number of $CO_2$ moles to $NO$ moles is $n_{CO_2}:n_{NO}=1:1$.

Step2: Analyze the properties of the gas samples

The average kinetic energy of gas molecules is given by $\overline{KE}=\frac{3}{2}kT$, where $k$ is the Boltzmann constant and $T$ is the temperature. Since the temperature of both gas samples is the same ($T = 273\ K$), the gas molecules have the same average kinetic energy. The molar mass of $CO_2$ is $M_{CO_2}=44\ g/mol$ and the molar mass of $NO$ is $M_{NO}=30\ g/mol$, so they do not have the same molar mass. And since the molar masses are different, even though the number of moles is the same, the masses ($m = nM$) are different. The root - mean - square speed is $v_{rms}=\sqrt{\frac{3RT}{M}}$, and since the molar masses are different, the speeds of the molecules are different.

Answer:

1. 1:1
2. Molecules with the same average kinetic energy