# Problem: Find the percent ionization of a 0.337 M HF solution. The Ka for HF is 3.5 x 10-4. A) 4.7% B) 3.2% C) 1.2 x 10-2% D) 3.5 x 10-2%E) 1.1 %

###### FREE Expert Solution

HF(aq) + H2O(l)  F(aq) + H3O+(aq); Ka = 3.5 × 10–4

From this, we can construct an ICE table. Remember that liquids are ignored in the ICE table and Ka expression.

The Ka expression for HF is:

$\overline{){{\mathbf{K}}}_{{\mathbf{a}}}{\mathbf{=}}\frac{\mathbf{products}}{\mathbf{reactants}}{\mathbf{=}}\frac{\mathbf{\left[}{\mathbf{H}}_{\mathbf{3}}{\mathbf{O}}^{\mathbf{+}}\mathbf{\right]}\mathbf{\left[}{\mathbf{F}}^{\mathbf{-}}\mathbf{\right]}}{\mathbf{\left[}\mathbf{HF}\mathbf{\right]}}}$

Plugging in the equilibrium concentrations from the ICE table into the Ka expression:

${\mathbf{K}}_{\mathbf{a}}\mathbf{=}\mathbf{3}\mathbf{.}\mathbf{5}\mathbf{×}{\mathbf{10}}^{\mathbf{-}\mathbf{4}}\mathbf{=}\frac{\mathbf{\left[}{\mathbf{H}}_{\mathbf{3}}{\mathbf{O}}^{\mathbf{+}}\mathbf{\right]}\mathbf{\left[}{\mathbf{F}}^{\mathbf{-}}\mathbf{\right]}}{\mathbf{\left[}\mathbf{HF}\mathbf{\right]}}$

${\mathbf{K}}_{\mathbf{a}}\mathbf{=}\mathbf{3}\mathbf{.}\mathbf{5}\mathbf{×}{\mathbf{10}}^{\mathbf{-}\mathbf{4}}\mathbf{=}\frac{\mathbf{\left(}\mathbf{x}\mathbf{\right)}\mathbf{\left(}\mathbf{x}\mathbf{\right)}}{\mathbf{0}\mathbf{.}\mathbf{337}\mathbf{-}\mathbf{x}}$

Now, we need to determine if we can remove (–x) from the equation. To do so, we need to determine the ratio of the initial concentration and Ka:

$\frac{\mathbf{\left[}\mathbf{HF}{\mathbf{\right]}}_{\mathbf{initial}}}{{\mathbf{K}}_{\mathbf{a}}}\mathbf{>}\mathbf{500}$

Since the ratio is greater than 500, we can remove (–x) from the equation.

The equation simplifies to:

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###### Problem Details

Find the percent ionization of a 0.337 M HF solution. The Ka for HF is 3.5 x 10-4

A) 4.7%

B) 3.2%

C) 1.2 x 10-2

D) 3.5 x 10-2%

E) 1.1 %