5 moles of $AB_{2}$ weigh $125 \times 10^{-3} \mathrm{~kg}$ and 10 moles of $A_{2} B_{2}$ weigh $300 \times 10^{-3} \mathrm{~kg}$. The molar mass of $A\left(M_{A}\right)$ and molar mass of $B\left(M_{B}\right)$ in $\mathrm{kg} \mathrm{mol}^{-1}$ are :

(C) $\mathrm{M}_{\mathrm{A}}=5 \times 10^{-3}$ and $\mathrm{M}_{\mathrm{B}}=10 \times 10^{-3}$

(A) $\mathrm{M}_{\mathrm{A}}=50 \times 10^{-3}$ and $\mathrm{M}_{\mathrm{B}}=25 \times 10^{-3}$

(B) $\mathrm{M}_{\mathrm{A}}=10 \times 10^{-3}$ and $\mathrm{M}_{\mathrm{B}}=5 \times 10^{-3}$

(D) $\mathrm{M}_{\mathrm{A}}=25 \times 10^{-3}$ and $\mathrm{M}_{\mathrm{B}}=50 \times 10^{-3}$

JEE Main · 2019 · 12 Apr 2019 · Shift 1 · Some Basic Concepts of Chemistry

5 moles of

A B_{2}

weigh

125 \times 1 0^{- 3} kg

and 10 moles of

A_{2} B_{2}

weigh

300 \times 1 0^{- 3} kg

. The molar mass of

A (M_{A})

and molar mass of

B (M_{B})

kg mol^{- 1}

are :

Answer: (C)

From

5

moles of

AB X_{2}

weighing

125 \times 1 0^{- 3} kg

, one mole weighs

25 \times 1 0^{- 3} kg

, so

M_{A} + 2 M_{B} = 25 \times 1 0^{- 3}

. From

10

moles of

A X_{2} B X_{2}

weighing

300 \times 1 0^{- 3} kg

, one mole weighs

30 \times 1 0^{- 3} kg

, so

2 M_{A} + 2 M_{B} = 30 \times 1 0^{- 3}

, i.e.

M_{A} + M_{B} = 15 \times 1 0^{- 3}

. Subtracting the second from the first gives

M_{B} = 10 \times 1 0^{- 3} kg mol^{- 1}

, and then

M_{A} = 15 \times 1 0^{- 3} - 10 \times 1 0^{- 3} = 5 \times 1 0^{- 3} kg mol^{- 1}

JEE Main · 2019 · 12 Apr 2019 · Shift 1 · Single correct option