Question

prove that pi=xi ptot where pi and xi are the partial pressure and mole fraction of the gas and plot is the total pressure exerted by n number of non reacting gases​

Answer 1

Answer:

(a) Ideal gas equation for individual gases-

$PV=nRT.....(1)$

Ideal gas equation for the mixture-

$P </p><p>total</p><p> </p><p> V=n </p><p>total</p><p> </p><p> RT.....(1)$

Dividing equation (1) by (2), we have

$\frac{PV}{ptotalv} = \frac{nrt}{ntotalrt}$

$\frac{p}{ptotal} = \frac{n}{ntotal}$

As we know that molar fraction of a gas is-

$X= \frac{ n </p><p>total}{n} </p><p></p><p> </p><p> .....(4)$

From equation (3)&(4), we have

$P=XP </p><p>total</p><p> </p><p> ⇒ Required relation$

Hence the relation between partial pressure and mole fraction of a gas is-

$P=XP </p><p>total</p><p>$

$(p \times \frac{a {n}^{2} }{ {v}^{2} } )(v - nb) = nrt$

for 1 mole, i.e.,

n=1

Substituting the value of n in equation (1), we get

$(p \times \frac{a {}^{} }{ {v}^{2} } )(v - b) = rt$

Hene Vander Waal's equation for 1 mole of a gas is-

Explanation:

$(p \times \frac{a {}^{} }{ {v}^{2} } )(v - b) = rt$