Question

A mixture of He, Ne, and Ar gases at a particular temperature has partial pressures of 0.75 atm He, 0.30 atm Ne, and 0.62 atm Ar. Which of the following shows the correct trend for the mole fractions of the component gases?

A. LaTeX: \chi_{Ne}<\chi_{Ar}<\chi_{He}B. LaTeX: \chi_{Ar}<\chi_{Ne}<\chi_{He}C. LaTeX: \chi_{He}<\chi_{Ar}<\chi_{Ne}D. LaTeX: \chi_{He}<\chi_{Ne}<\chi_{Ar}

Answer 1

The order of mole fraction in increasing order will be:

`\chi_(Ne)<\chi_(Ar)<\chi_(He)`

Step-by-step explanation:

Relation between mole fraction and partial pressure of the component is given as:

`p_i=P* \chi_i`

Where :P = Total pressure of the mixture

`p_i` = partial pressure of the i component

`\chi_i` = Mole fraction of the i component

We have :

Partial pressure of the helium gas ,
`p_(He)`= 0.75 atm

Partial pressure of the neon gas,
`p_(Ne)`= 0.30 atm

Partial pressure of the argon gas ,
`p_(Ar)`= 0.62 atm

As we can see that from the above equation, that partial pressure and mole fraction are directly linked to each other.

`p_i\propto \chi_i`

So, the gas with higher value of partial; pressure will have higher value of mole fraction in the mixture.

So, the order of partial pressure from lowest to highest is:

`p{Ne}<p_(Ar)<p_(He)`

And hence the order of mole fraction will also be same :

`\chi_(Ne)<\chi_(Ar)<\chi_(He)`