# $5\: moles$ of $AB_2$  weigh $125\times 10^{-3}kg$ and $10\: moles$ of $A_2B_2$ weigh $300\times 10^{-3}kg.$ The molar mass of $A(M_A)$ and molar mass of $B(M_B)$ in $kg\: mol^{-1}$ are : Option 1)$M_A=50\times 10^{-3}\: \: and\: \: M_B=25\times 10^{-3}$Option 2)$M_A=25\times 10^{-3}\: \: and\: \: M_B=50\times 10^{-3}$Option 3)$M_A=5\times 10^{-3}\: \: and\: \: M_B=10\times 10^{-3}$  Option 4)$M_A=10\times 10^{-3}\: \: and\: \: M_B=5\times 10^{-3}$

Molar Mass -

The mass of one mole of a substance in grams is called its molar mass.

- wherein

Molar mass of water = 18 g mol-1

Mole Concept -

One mole is the amount of a substance that contains as many particles or entities as there are atoms in exactly 12 g (or 0.012 kg) of the 12C isotope.

- wherein

one mole = 6.0221367 X 1023

Let atomic mass of $A = x$  & atomic mass of $B = y$

$\therefore \: \: \: For\: \: AB_2:$

$5\left ( x+2y \right )=125g\Rightarrow x+2y=25g\cdots (I)$

$For\: \: A_2B_2$ :

$10\left ( 2x+2y \right )=300g$

$\Rightarrow x+y=15g\cdots \cdots (II)$

Solving equations (I) & (II), simultaneously, we get:

$x=5\times 10^{-3}kg$     &     $y=10\times 10^{-3}kg$

Thus, $M_A=5\times 10^{-3}kg$

$M_B=10\times 10^{-3}kg$

Option 1)

$M_A=50\times 10^{-3}\: \: and\: \: M_B=25\times 10^{-3}$

Option 2)

$M_A=25\times 10^{-3}\: \: and\: \: M_B=50\times 10^{-3}$

Option 3)

$M_A=5\times 10^{-3}\: \: and\: \: M_B=10\times 10^{-3}$

Option 4)

$M_A=10\times 10^{-3}\: \: and\: \: M_B=5\times 10^{-3}$

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