What mass of ammonium chloride, NH4Cl, (Ka = 5.6 x 10^-10) must be added to exactly 500mL of 0.10M

What mass of ammonium chloride, NH4Cl, (Ka = 5.6 x 10^-10) must be added to exactly 500mL of 0.10M NH3 solution to give a solution with a pH of 9.00?

Concepts and reason
The concept used to solve this problem is based on the chemical equilibrium.
The pH of solution is used to determine acidity and basicity of a solution.

Fundamentals
The pH of solution can be determine by Henderson-Hasselbalch equation as follow.
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Answer:
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Write the balanced equilibrium reaction as follow.
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Now, Henderson-Hasselbalch equation for this reaction is written as follow.
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Explanation:
The Henderson-Hasselbalch equation is used to calculate pH of solution by using concentrations of base and its conjugate acid.