A student mixes 45.0 ml of .150 M HCL with 30.0 ml of .200 M NaOH. What is the pH of the resulting solution?
mol HCl = 0.150 x 0.0450 = 0.00675
mol NaOH = 0.200 x 0.0300 = 0.00600
...........HCl + NaOH ==>NaCl + H2O
initial..0.00675.0.00600.....0.....0
change..-0.006...-0.006...0.006..0.006
equil....0.00075..........0.006..0.006
You can see that thae HCl is in excess so (HCl) = (H^+) = 0.00075/total volume in liters. Then convert to pH = -log(H^+).
To find the pH of the resulting solution, we need to calculate the concentration of the resulting solution first.
Step 1: Calculate the moles of acid (HCl):
HCl concentration = 0.150 M
Volume of HCl = 45.0 ml = 0.045 L (converted to liters)
moles of HCl = concentration * volume = 0.150 M * 0.045 L = 0.00675 moles
Step 2: Calculate the moles of base (NaOH):
NaOH concentration = 0.200 M
Volume of NaOH = 30.0 ml = 0.030 L (converted to liters)
moles of NaOH = concentration * volume = 0.200 M * 0.030 L = 0.006 moles
Step 3: Determine the limiting reagent:
To determine the limiting reagent, we compare the moles of acid and base. The reactant with the smaller number of moles is the limiting reagent.
In this case, both substances (HCl and NaOH) react in a 1:1 ratio, so the limiting reagent is NaOH because it has fewer moles (0.006 moles).
Step 4: Calculate the moles of excess acid/base:
To calculate the moles of excess acid/base, we subtract the moles of the limiting reagent from the initial moles.
moles of excess HCl = moles of HCl - moles of NaOH = 0.00675 moles - 0.006 moles = 0.00075 moles
Step 5: Calculate the concentration of the resulting solution:
The volume of the resulting solution is the sum of the initial volumes.
Initial volume of HCl = 45.0 ml = 0.045 L
Initial volume of NaOH = 30.0 ml = 0.030 L
Total volume of resulting solution = 0.045 L + 0.030 L = 0.075 L
The concentration of the resulting solution is the total moles divided by the total volume.
Concentration of resulting solution = Total moles / Total volume
= (moles of NaOH + moles of excess HCl) / Total volume
= (0.006 moles + 0.00075 moles) / 0.075 L
= 0.007 moles / 0.075 L
= 0.0933 M
Step 6: Calculate pH using the concentration of the resulting solution.
The pH of a solution can be calculated using the formula: pH = -log[H+]
In this case, since we have hydrochloric acid (HCl), which is a strong acid and completely dissociates in water, the concentration of H+ ions is equal to the concentration of the resulting solution.
pH = -log[0.0933]
= -log(0.0933)
= 1.03
So, the pH of the resulting solution is approximately 1.03.