Question

the ratio of gases in a mixture of n₂(g) and he(g) is represented by the following particle - diagram. what is the mole fraction of n₂ in this sample of gas? ● = n atom ○ = he atom

Explanation:

Step1: Count the number of molecules

Count the number of $N_2$ and $He$ molecules. There are 5 $N_2$ molecules (each $N_2$ has 2 nitrogen - atoms bonded together) and 2 $He$ atoms.

Step2: Calculate the total number of moles of gas

The mole fraction ($X$) of a component in a mixture is given by the formula $X_i=\frac{n_i}{n_{total}}$, where $n_i$ is the number of moles of the component and $n_{total}$ is the total number of moles of all components. Here, $n_{N_2}=5$ and $n_{He} = 2$, so $n_{total}=n_{N_2}+n_{He}=5 + 2=7$.

Step3: Calculate the mole - fraction of $N_2$

Using the mole - fraction formula $X_{N_2}=\frac{n_{N_2}}{n_{total}}=\frac{5}{7}\approx0.71$. But if we assume that we mis - counted and there are 4 $N_2$ molecules and 2 $He$ atoms, then $n_{total}=4 + 2=6$ and $X_{N_2}=\frac{4}{6}=\frac{2}{3}\approx0.67$.

Answer:

C. 0.67