Calculate the pH of a 0.05 M NH4Cl solution (Kb for NH3 = 1.8 x 10^-5).

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Question: Calculate the pH of a 0.05 M NH4Cl solution (Kb for NH3 = 1.8 x 10^-5).

Options:

Correct Answer: 5.25

Solution:

Using the formula for weak bases, pH = 14 - 0.5(pKb - logC) = 14 - 0.5(4.74 - log(0.05)) = 5.25.

Calculate the pH of a 0.05 M NH4Cl solution (Kb for NH3 = 1.8 x 10^-5).

Calculate the pH of a 0.05 M NH4Cl solution (Kb for NH3 = 1.8 x 10^-5).

Step 1: Identify the concentration of the NH4Cl solution, which is 0.05 M.
Step 2: Recognize that NH4Cl is a salt that comes from a weak base (NH3) and a strong acid (HCl). This means it will create an acidic solution.
Step 3: Find the Kb value for NH3, which is given as 1.8 x 10^-5.
Step 4: Calculate the pKb using the formula pKb = -log(Kb). So, pKb = -log(1.8 x 10^-5). This gives approximately 4.74.
Step 5: Use the formula for calculating pH from pKb: pH = 14 - 0.5(pKb - logC), where C is the concentration of the solution (0.05 M).
Step 6: Calculate log(0.05). This is approximately -1.3.
Step 7: Substitute the values into the formula: pH = 14 - 0.5(4.74 - (-1.3)).
Step 8: Simplify the equation: pH = 14 - 0.5(4.74 + 1.3) = 14 - 0.5(6.04).
Step 9: Calculate 0.5(6.04) = 3.02.
Step 10: Finally, calculate pH = 14 - 3.02 = 10.98.

Acid-Base Chemistry – Understanding the relationship between weak acids and their conjugate bases, and how to calculate pH using Kb and concentration.
pH Calculation – Applying the formula for calculating pH from the concentration of a weak base and its Kb value.
Conjugate Acid-Base Pairs – Recognizing that NH4Cl is a salt that dissociates into NH4+ (a weak acid) and Cl- (a neutral ion).