Question

the mole fraction of benzene in a solution with toluene is 0.50 .calculate the mole fraction of toluene

Answer 1

$\large{\underline{\underline{\red{\tt{\purple{\leadsto } AnsweR:-}}}}}$

Given that the mole fraction of benzene in a solution with toluene is 0.50. And we need to Find the mole fraction of toluene .

$\tt As\: we \:know \:that \::-$

$\large\boxed{\red{\qquad\green{\dag} \bf \chi_{\footnotesize{A}} + \chi_B = 1\qquad}}$

Using this ,

$\tt:\implies \chi_{benzene} + \chi_{toluene} = 1$

$\tt:\implies 0.50 +\chi_{toluene}=1$

$\tt:\implies \chi_{toluene}=1-0.5$

$\underline{\boxed{\red{\tt{\longmapsto \: \chi_{toluene}\:=\:0.5 }}}}$

$\boxed{\green{\sf \pink{\dag} Hence\: the\:mole\: fraction\:of\: toluene\:is\:0.5.}}$

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$\large{\underline{\underline{\red{\tt{\purple{\leadsto } MorE\:to\: Know:-}}}}}$

$\underline{\blue{\bf\leadsto Mole\: Fraction}}$

It is defined as the number of moles of solute by number of moles of solution. We can also calculate partial pressure exerted by gases using mole fraction.

$\bf\qquad\qquad If \: we\: denote \:,$

• $\sf Number\:of\:moles \:of\: first\:sol^n\:=\:n_A$
• $\sf Number\:of\:moles \:of\: second\:sol^n\:=\:n_B$
• $\sf Number\:of\:moles \:of\: whole\:sol^n\:=\:n_A+n_B$

$\tt Mole\: Fraction\:will\:be:-$

$\underline{\pink{\sf \purple{\hookrightarrow}Mole\: Fraction\:of\:A }}$

$\large\boxed{\red{\green{\dag} \bf \chi_{\footnotesize{A}}=\dfrac{n_A}{n_A+n_B} }}$

$\underline{\pink{\sf \purple{\hookrightarrow}Mole\: Fraction\:of\:B}}$

$\large\boxed{\red{\green{\dag} \bf \chi_{\footnotesize{B}}=\dfrac{n_B}{n_A+n_B} }}$

______________________________

If we know the mole fraction of any one of them , then we can simply subtract it from 1 to obtain the mole fraction of second solutions.

$\bf \qquad\qquad Proof :-$

$\tt:\implies \chi_A+\chi_B=1$

$\tt:\implies \dfrac{n_A}{n_A+n_B}+\dfrac{n_B}{n_A+n_B}=1$

$\tt:\implies\cancel{ \dfrac{n_A+n_B}{n_A+n_B}}=1$

$\underline{\boxed{\red{\tt{\longmapsto \: 1=1 }}}}$

$\boxed{\green{\sf \pink{\dag} Hence\: Proved}}$