Solid NaOH is added to 1 L of 0.05 M aqueous solution of $H_{2} S$ until the pH reached a value of 12.0. Calculate the total mass of solid NaOH added (in gm).
(For H₂S: $K_{a 1} = 1 \times 1 0^{- 7}$ , $K_{a 2} = 1.0 \times 1 0^{- 14}$ )

Question

Solid NaOH is added to 1 L of 0.05 M aqueous solution of $H_{2} S$ until the pH reached a value of 12.0. Calculate the total mass of solid NaOH added (in gm).

(For H₂S: $K_{a 1} = 1 \times 1 0^{- 7}$ , $K_{a 2} = 1.0 \times 1 0^{- 14}$ )

TestHub · Accepted Answer

Given data: At pH = 12, [ H + ] = 1 0 − 12 M and [ O H − ] = 1 0 − 2 M. Concentration of species: From K a 1 ​ and K a 2 ​ , we have [ H S − ] = [ H + ] K a 1 ​ ​ [ H 2 ​ S ] = 1 0 5 [ H 2 ​ S ] and [ S 2 − ] = [ H + ] K a 2 ​ ​ [ H S − ] = 0.01 [ H S − ] . Mass balance: Since [ H 2 ​ S ] ≈ 0 , total sulfur concentration C = [ H S − ] + 0.01 [ H S − ] = 0.05 M ⟹ [ H S − ] ≈ 0.0495 M and [ S 2 − ] ≈ 0.0005 M. Charge balance: [ N a + ] = [ O H − ] + [ H S − ] + 2 [ S 2 − ] = 0.01 + 0.0495 + 2 ( 0.0005 ) = 0.0605 M. Final Mass Calculation: Mass of NaOH = Moles × Molar mass = 0.0605 moles × 40 g/mol ≈ 2.41gm .

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