At $291 \ K$,a saturated solution of $BaSO_4$ was found to have a specific conductivity of $3.648 \times 10^{-6} \ \Omega^{-1} \ cm^{-1}$ and that of the water used is $1.25 \times 10^{-6} \ \Omega^{-1} \ cm^{-1}$. If the ionic conductances of $Ba^{2+}$ and $SO_4^{2-}$ are $110$ and $136.6 \ \Omega^{-1} \ cm^2 \ mol^{-1}$ respectively,the solubility of $BaSO_4$ at $291 \ K$ will be (Atomic masses: $Ba=137, S=32, O=16$)

• A
  $1.435 \times 10^{-3} \ g \ L^{-1}$
• B
  $2.266 \times 10^{-3} \ g \ L^{-1}$
• C
  $2.843 \times 10^{-3} \ g \ L^{-1}$
• D
  $1.768 \times 10^{-3} \ g \ L^{-1}$