When 50 mL of 0.01 M weak base ( BOH ) solution is mixed with 50 mL of 0.1 M of its salt ( BCl ) solution, the pH of the resultant solution is found to be 9 . The dissociation constant of the base is x 10⁻⁶ . The value of x is _______.

Step-by-step solution

The given mixture forms a basic buffer. Given pH = 9 , the pOH of the solution is: pOH = 14 - pH = 14 - 9 = 5 Millimoles of weak base BOH = 50 0.01 = 0.5 mmol Millimoles of salt BCl = 50 0.1 = 5 mmol Using the Henderson-Hasselbalch equation for a basic buffer: pOH = p K_ b + ( [ Salt ] [ Base ] ) 5 = p K_ b + ( 5 0.5 ) 5 = p K_ b + (10) 5 = p K_ b + 1 p K_ b = 4 K_ b = 10⁻⁴ = 100 10⁻⁶ Comparing with x 10⁻⁶ , we get x = 100 . Answer: 100