0.05 mole of HCL is added to a liter of buffer containing 0.04 mole of NH3 and 0.03 mole of NH4CL. What is the ph? Kb= 1.8X10^-5
To find the pH of the buffer solution after adding 0.05 mol of HCl, we need to consider the reaction between NH3 (ammonia) and HCl (hydrochloric acid) and calculate the change in concentration of NH3 and NH4Cl.
The balanced equation for the reaction between NH3 and HCl is:
NH3 + HCl → NH4Cl
According to the stoichiometry of the balanced equation, for every 1 mol of HCl that reacts, 1 mol of NH3 is consumed, and 1 mol of NH4Cl is produced. Therefore, after adding 0.05 mol of HCl, the concentration of NH3 will decrease by 0.05 mol, and the concentration of NH4Cl will increase by 0.05 mol.
Initially, the concentration of NH3 is 0.04 mol, and the concentration of NH4Cl is 0.03 mol. After the reaction, the concentration of NH3 will be (0.04 - 0.05) mol = -0.01 mol, which is not physically possible. This means that all the NH3 will be consumed, and the concentration of NH4Cl will increase by 0.05 mol, resulting in a final concentration of 0.03 + 0.05 = 0.08 mol.
Now, let's calculate the concentration of OH- ions using the Kb value. Kb represents the base dissociation constant for the reaction of NH3 with water:
Kb = [NH4+][OH-] / [NH3]
Since we know the concentration of NH4+ (which is equal to the concentration of NH4Cl), we can rearrange the equation to solve for [OH-]:
[OH-] = (Kb * [NH3]) / [NH4+]
[OH-] = (1.8 * 10^-5 * 0.04) / 0.08
[OH-] = 9 * 10^-6
Since this is a basic solution, the concentration of OH- ions is directly related to the concentration of H+ ions through the equation:
[OH-] * [H+] = Kw
Kw is the ion product of water, which is equal to 1.0 * 10^-14 at 25 degrees Celsius. Therefore, we can solve for [H+] as follows:
[OH-] * [H+] = 1.0 * 10^-14
[H+] = (1.0 * 10^-14) / [OH-]
[H+] = (1.0 * 10^-14) / (9 * 10^-6)
[H+] = 1.1 * 10^-9
To find the pH, we take the negative logarithm (base 10) of the [H+] concentration:
pH = -log([H+])
pH = -log(1.1 * 10^-9)
pH = 8.96
Therefore, the pH of the buffer solution after adding 0.05 mol of HCl is approximately 8.96.