### Calculate the concentration, given the percent dissociation

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**Problem #1:** What must be the molarity of an aqueous solution of NH_{3} if it is 4.1% ionized?

**Solution:**

K_{b} = ([NH_{4}^{+}] [OH¯]) / [NH_{3}]
1.77 x 10^{-5} = [(0.041x) (0.041x)] / (x)

0.001681x^{2} = 1.77 x 10^{-5}x

0.001681x^{2} - 0.0000177x = 0

Use this quadratic equation root solver.

x = 0.0105 M

Comment: note that the value for the K_{b} is not provided in the problem, but is required for the solution. The K_{b} for ammonia is available in many references soures.

**Problem #2:** Determine the molar concentration for an acetic acid (CH_{3}COOH) solution known to be 3.5% dissociated. The K_{a} is 1.77 x 10^{-5}

**Solution:**

K_{a} = ([H^{+}] [CH_{3}COO¯]) / [CH_{3}COOH]
1.77 x 10^{-5} = [(0.035x) (0.035x)] / (x)

0.001225x^{2} = 1.77 x 10^{-5}x

0.001225x^{2} - 0.0000177x = 0

Use this quadratic equation root solver.

x = 0.0144 M

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