The expression relating mole fraction of solute ( $x_{2}$ ) and molarity ( $M$ ) of the solution is:

x_{2} = \frac{M M_{1}}{M (M_{1} - M_{2}) + p}

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x_{2} = \frac{M M_{1}}{M (M_{1} - M_{2}) - p}

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x_{2} = \frac{M (M_{1} - M_{2}) + p}{M M_{1}}

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x_{2} = \frac{M (M_{1} - M_{2}) - p}{M M_{1}}

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Solution

The correct option is B $x_{2} = \frac{M M_{1}}{M (M_{1} - M_{2}) + p}$
Let land 2 denote solvent and solute respectively,
$x_{2} = \frac{n_{2}}{n_{1} + n_{2}} = \frac{n_{2}}{\frac{m_{1}}{M_{1}} + n_{2}}$
= $\frac{n_{2} M_{1}}{m_{1} + n_{2} M_{1}}$ = $\frac{n_{2} M_{1}}{(m_{1} + m_{2}) + n_{2} M_{1} - m_{2}}$
= $\frac{n_{2} M_{1}}{V_{e} + n_{2} M_{1} - m_{2}}$ = $\frac{n_{2} M_{1}}{V_{p} + n_{2} (M_{1} - M_{2})}$
= $\frac{(n_{2} / v) M_{1}}{p + (n_{2} / v) (M_{1} - M_{2})}$ = $\frac{M M_{1}}{p + M (M_{1} - M_{2})}$

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The expression relating mole fraction of solute (x2) and molarity (M) of the solution is:

The correct option is B x2=MM1M(M1−M2)+pLet land 2 denote solvent and solute respectively,x2=n2n1+n2=n2m1M1+n2=n2M1m1+n2M1= n2M1(m1+m2)+n2M1−m2=n2M1Ve+n2M1−m2 =n2M1Vp+n2(M1−M2)=(n2/v)M1p+(n2/v)(M1−M2) = MM1p+M(M1−M2)

The expression relating mole fraction of solute ( $x_{2}$ ) and molarity ( $M$ ) of the solution is: