What is the concentration of $\mathrm{OH}^{-}$ion in a solution containing $0.05 \mathrm{M}…

What is the concentration of $\mathrm{OH}^{-}$ion in a solution containing $0.05 \mathrm{M} \mathrm{H}^{+}$ions?
  1. $2.5 \times 10^{-13} \mathrm{M}$
  2. $5.0 \times 10^{-2} \mathrm{M}$
  3. $2.0 \times 10^{-13} \mathrm{M}$
  4. $4.2 \times 10^{-12} \mathrm{M}$

Solution

$\begin{array}{ll} & \mathrm{K}_{\mathrm{w}}=\left[\mathrm{H}_3 \mathrm{O}^{+}\right]\left[\mathrm{OH}^{-}\right] \\ \therefore \quad & 10^{-14}=0.05 \times\left[\mathrm{OH}^{-}\right] \\ & {\left[\mathrm{OH}^{-}\right]=\frac{10^{-14}}{0.05}} \\ & {\left[\mathrm{OH}^{-}\right]=2.0 \times 10^{-13} \mathrm{M}}\end{array}$

Asked in: MHT CET 2023 (11 May Shift 1)

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