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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

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.