A chemist titrates 110.0 mL of a 0.5568 M ammonia (NH_3) solution with 0.4412 M HCl solution at 25 degree C. Calculate the pH at equivalence. The pK_b of ammonia is 4.75. Round your answer to 2 decimal places. Note for advanced students: you may assume the total volume of the solution equals the initial volume plus the volume of HCl solution added. pH =

pH = 4.93

Explanation:

Step 1: Data given

Volume of a 0.5568 M ammonia NH3 solution = 110.0 mL = 0.110 L

Molarity of HCl = 0.4412 M

pKb ammonia = 4.75

Step 2: The balanced equation

NH3 + HCl ⇒ NH4+ + Cl-

Step 3: Calculate moles NH3

Moles NH3 =  molarity NH3 * volume

Moles NH3 = 0.5568 M * 0.110 L

Moles NH3 = 0.06125 moles

Step 3: Calculate moles HCl needed

For 0.06125 moles NH3 we need 0.06125 moles HCl

Step 4: Calculate volume HClFor 1 mol NH3 we need 1 mol HCl to produce 1 mol NH4+

Volume HCl = moles HCl / molarity

Volume HCl = 0.06125 moles / 0.4412 M

Volume HCl = 0.139 L = 139 mL

Step 5: Calculate total volume

Total volume = 110.0 mL + 139 mL

Total volume = 249 mL

Step 6: Calculate moles NH4+

For 1 mol NH3 we need 1 mol HCl to produce 1 mol NH4+

For 0.06125 moles NH3 we'll have 0.06125 moles NH4+

Step 7: Calculate [NH4+]

[NH4+] = moles NH4+ / volume

[NH4+] = 0.06125 moles / 0.249 L

[NH4+]= 0.246 M

Step 8: The equation

NH4+ + H2O → NH3 + H3O+

Step 9: The initial concentration

[NH4+] = 0.246 M

[NH3]= 0M

[H30+] = 0M

Step 10: Calculate the concentration at the equilibrium

[NH4+] = 0.246 - X M

[NH3]= X M

[H30+] = X M

Step 11: Calculate Ka

pKa = 14 - pKb

pKa = 14 - 4.75 = 9.25

Ka = 10^-9.25 = 5.6 *10^-10

Ka = [NH3][H3O+] / [NH4+]

Ka = X² / (0.246 - X)

5.6 *10^-10 = X² / (0.246 - X)

5.6 *10^-10 = X² / (0.246)

X = 1.17*10^-5 M = [ H3O+]

Step 12: Calculate pH

pH = - log [1.17*10^-5]

pH = 4.93

mechanics (greek   is that area of science concerned with the behaviour of physical bodies when subjected to forces or displacements, and the subsequent effects of the bodies on their environment. the scientific discipline has its origins in ancient greece with the writings of aristotle and archimedes[1][2][3] (see history of classical mechanics and timeline of classical mechanics). during the early modern period, scientists such as galileo, kepler, and newton laid the foundation for what is now known as classical mechanics. it is a branch of classical physics that deals with particles that are either at rest or are moving with velocities significantly less than the speed of light. it can also be defined as a branch of science which deals with the motion of and forces on objects. the field is yet less widely understood in terms of quantum theory.

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