Express partial pressure in terms of mole fraction.

Explanation

Suppose at the temperature T, three gases enclosed in the volume V, having partial pressure `p_(1),p_(2),p_(3)` respectively.
`p_(1)=(n_(1)RT)/(V)" " …(i)`
`p_(2)=(n_(2)RT)/(V)" " …(ii)`
`p_(3)=(n_(3)RT)/(V)" " ...(iii)`
Where, `n_(1),n_(2)` and `n_(3)` are number of moles of these gases.
`p_("Total")=p_(1)+p_(2)+p_(3)`
Substituting the values of `p_(1),p_(2)` and `p_(3)`, we get
`="n"_(1)(RT)/(V) +"n"_(2)(RT)/(V)+"n"_(3)(RT)/(V) = (n_(1)+n_(2)+n_(3)) (RT)/(V)" " ...(iv)`
On dividing `p_(1)` by `p_("Total")`, we get
`p_(1)=(n_(1))/(n_(1)+n_(2)+n_(3)) =(n_(1))/(n) =x_(1)`
Where, `n=n_(1)+n_(2)+n_(3)`
`x_(1)` is called mole fraction of first gas.
Here `p_(1)=x_(1) p_("Total")`
`p_(2)=x_(2)p_("Total") and p_(3)=x_(3)p_("Total")`
Thus a general equation can be written as `p_(i)=x_(i)p_("Total")`
Where, `p_(i)` and `x_(i)` are partial pressure and mole fraction of `i^(th)` gas respectively.