Suppose 95.0 mL of HCl gas at 25 ºC and 707 torr is bubbled into 298 mL of pure water. What will be the pH of the resulting solution, assuming all the HCl dissolves in the water?
Use PV = nRT and solve for n = number mols HCl.
The M HCl = mols HCl/L solution.
Then pH = -log(HCl)
(0.930atm*0.393L)/(0.0821*298)= 0.0149mol
0.0149mol/0.393L= 0.038
-log(0.038)= 1.42
what did I do wrong?
To find the pH of the resulting solution, you need to calculate the concentration of HCl in the solution first. Here's how you can do it:
Step 1: Convert the volume of HCl gas to moles using the ideal gas law.
The ideal gas law equation is PV = nRT, where:
P = pressure (in atm)
V = volume (in L)
n = moles of gas
R = ideal gas constant (0.0821 L⋅atm/(mol⋅K))
T = temperature (in Kelvin)
Given:
Volume of HCl gas (V_HCl) = 95.0 mL = 0.095 L
Pressure of HCl gas (P_HCl) = 707 torr
Temperature (T) = 25 ºC = 298 K (convert to Kelvin)
Convert the pressure to atm:
P_HCl = 707 torr * (1 atm / 760 torr) = 0.929 atm
Now, rearrange the ideal gas law equation to solve for moles (n):
n = PV / RT
n_HCl = (0.929 atm * 0.095 L) / (0.0821 L⋅atm/(mol⋅K) * 298 K)
Step 2: Calculate the concentration of HCl in the solution.
Concentration (C) is defined as moles of solute per volume of solution. Since the HCl completely dissolves in water, the volume of water (V_water) will be the total volume of the resulting solution.
Given:
Volume of water (V_water) = 298 mL = 0.298 L
Moles of HCl (n_HCl) = calculated in Step 1
C_HCl = n_HCl / V_water
Step 3: Calculate the pH of the solution.
The pH is a measure of the concentration of hydrogen ions (H+). Since HCl is a strong acid, it completely dissociates in water to produce H+ ions.
pH is defined as the negative logarithm (base 10) of the concentration of H+ ions.
pH = -log[H+]
Knowing that HCl produces one H+ ion for every HCl molecule:
pH = -log(C_HCl)
Now, substitute the value of C_HCl from Step 2 into the equation to calculate the pH.