Question

The mass of sodium hydroxide that must be dissolved in \(1.0\,\text{L}\) solution to get pH of \(12\) is

• A. \(0.2\,\text{g}\)
• B. \(0.3\,\text{g}\)
• C. \(0.4\,\text{g}\)
• D. \(0.8\,\text{g}\)

Hint:

For aqueous solutions, \[ \boxed{\mathrm{pH+pOH}=14.} \] For strong bases, \[ \boxed{ [\mathrm{OH^-}] = [\mathrm{Base}]. } \]

Answer 1

The Correct Option is C

Step 1: Calculate the hydroxide ion concentration. Given, \[ \mathrm{pH}=12. \] Therefore, \[ \mathrm{pOH}=14-12=2. \] Hence, \[ [\mathrm{OH^-}] = 10^{-2}\,\mathrm{mol\,L^{-1}}. \]

Step 2: Find the number of moles of NaOH. Since NaOH is a strong base, \[ [\mathrm{NaOH}] = [\mathrm{OH^-}] = 10^{-2}\,\mathrm{mol\,L^{-1}}. \] For \[ 1.0\,\text{L}, \] \[ n = 10^{-2}\times1 = 0.01\;\text{mol}. \]

Step 3: Calculate the required mass. The molar mass of NaOH is \[ 40\;\mathrm{g\,mol^{-1}}. \] Thus, \[ m = 0.01\times40 = 0.4\;\text{g}. \] Hence, \[ \boxed{0.4\;\text{g}.} \] Therefore, the correct option is \(\boxed{(C)}\).