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$3$ mole of gas ''$X$" and 2 moles of gas "$Y$" enters from the end "$P$" and "$Q$" of the cylinder respectively. The cylinder has the area of cross section, shown as under
the length of the cylinder is $150cm$. The gas "$x$" intermixes with gas "$y$" at this point. If the molecular weight of the gases $x$ and $y$ is $20$ and $80$ respectively, then what will be the distance of point $A$ from $Q$?
(A) $75cm$
(B) $50cm$
(C) $37.5cm$
(D) $90cm$

Last updated date: 13th Jun 2024
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Hint: Molecular weight is an amount of the sum of the atomic weight values of the atoms in a molecule. Molecular weight is used in chemistry to define stoichiometry in chemical reactions and equations. Molecular weight is normally abbreviated by $M.W$ or $MW$. Molecular weight is either unit less or expressed in terms of atomic mass units (amu) or Daltons ($Da$).
Formula Used:
$\dfrac{{rx}}{{ry}} = \dfrac{{{w_x}}}{{{n_y}}}\sqrt {\dfrac{{{M_y}}}{{{M_x}}}} $

Complete Step by step solution:
So we know the equation
$\dfrac{{rx}}{{ry}} = \dfrac{{{w_x}}}{{{n_y}}}\sqrt {\dfrac{{{M_y}}}{{{M_x}}}} $
Here, ${M_x}$ and ${M_y}$ represent the molecular weight of the gasses $X$ and $Y$.
Now substituting the values in the above equation
$\dfrac{{rx}}{{ry}} = \dfrac{3}{2}\sqrt {\dfrac{{80}}{{20}}} = \dfrac{3}{1} = 3:1$
So distance travelled by the gas $X$ is $3$ and distance travelled by the gas $Y$ is $1$.
Hence it can be written as
$\dfrac{{dis\tan ce{\text{ }}travelled{\text{ }}by{\text{ }}gas{\text{ }}X}}{{dis\tan ce{\text{ }}travelled{\text{ }}by{\text{ }}gas{\text{ }}Y}} = 3:1$
So now we can calculate the distance of $A$ from $Q$.
$\therefore $ Distance of $A$ from $Q = \dfrac{{150}}{3} = 50cm$

Hence option B is correct

Additional Information
The molecular weight of a molecule or polymer is related to its properties. As the molecular weight increases their mechanical properties also increase. Every molecule has ideal weight and the different properties are optimized. The number of average molecular weights is stated as the total weight of a molecule divided by the total number of molecules.

The mole is the unit of measurement for the amount of substance in the International System of Units. A mole of a substance or a mole of particles is well-defined as exactly particles, which may be atoms, molecules, ions, or electrons. In short, for particles, $1mol = 6.02214076 \times {10^{23}}.$ Remember to find distance travelled by particle or molecule we will divide the length by number of particles or molecules given.