How to Calculate the pH of Ammonia Water Using KB

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Ammonia (NH3) is a gas that readily dissolves in water and behaves as a base. The ammonia equilibrium is describe with the equation NH3 + H2O = NH4(+) + OH(-). Formally, the acidity of the solution is expressed as pH. This is the logarithm of the concentration of hydrogen ions (protons, H+) in the solution. Base dissociation constant (Kb) is defined as Kb = [NH4+][OH-]/[NH3]. (Brackets refer to the molar concentration of ions or molecules in the solution.) Kb is a constant at a given temperature and is usually tabulated at 25 degrees Celsius. The Kb value for ammonia is 1.8E-5 (the notation “E-5” means “ten in power -5”).

    Multiply the Kb value by the total ammonia concentration and the number 4. The total concentration is the sum of [NH4+] and [NH3] in the solution. This concentration must be known or given in order to calculate pH. For example, the concentration is equal to 0.1 molar. Then the value in this Step should be calculated as 1.8E-5 x 0.1 x 4 = 7.2E-6.

    Take the square root of the value obtained in Step 1. In the example, it is sqrt(7.2E-6) = 2.683E-3. (Note that this result is rounded to thousandths.)

    Subtract the Kb value from the number obtained in Step 2 and then divide the result by 2 to calculate the concentration of the hydroxide ions (OH-). In our example, [OH-] = (2.683E-3 - 1.8E-5) /2 = 1.333E-3 molar.

    Divide the magnitude 1E-14 by the concentration of hydroxide ions (Step 3) to calculate the concentration of the protons [H+]: [H+] = 1E-14 / [OH-]. In our example, [H+] = 1E-14 / 1.333E-3 = 7.502E-11.

    Take the logarithm (with the base 10) of the proton concentration (Step 4), and multiply the result by -1 to calculate pH. In this example, pH = -1 x log(7.502E-11) = 10.12.

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