Equal volumes of 0.220 M weak base (Kb=4.0x10^-9) and 0.220 M HCl are mixed. Calculate the pH of the resulting solution
BOH = weak base
BOH + HCl ==> BCl + H2O
So the pH at the equivalence point will be the pH of a solution of the salt, BCl. The B^+ will be hydrolyzed to form
B^+ + HOH ==> BOH + H^+
Ka for B^+ = (Kw/Kb for BOH) - (H^+)(BOH)/(B^+)
(Kw/4.0E-9) = (x)(x)/(0.110-x)
and solve for x = (H^+) and convert to pH.
Where did the 0.110 come from. If you mix equal volumes of equal concns of acid and base you get 1/2 for the concn of the salt or 0.220/2 = 0.110.
Kw is 1E-14 . You probably can avoid a quadratic equation if you assume x will be small and call 0.110-x = 0.110.
Equal volumes of 0.220 M weak base ( 𝐾b=4.0×10−9 ) and 0.220 M HCl are mixed.
Calculate the pH of the resulting solution.
Oh, we've got a mixer here! Let's see what happens when these two get together. Okay, so we have a weak base and strong acid partying it up.
Since we're working with equal volumes, we can assume that the initial concentrations of both the base and the acid will be halved. Therefore, our final concentrations of the weak base and HCl will both be 0.110 M.
Now, let's focus on the weak base. We know its Kb value is 4.0x10^-9, so we can find its pOH using the equation:
pOH = -log(Kb) = -log(4.0x10^-9)
Calculating that, we get pOH = 8.4.
Since pH + pOH = 14, we subtract 8.4 from 14 to find the pH:
pH = 14 - 8.4
So the pH of our result will be approximately 5.6. Voila!
To calculate the pH of the resulting solution, we first need to determine the moles of the weak base and HCl that are present in the mixture.
Given:
- Volume of the mixture is equal for both the weak base and HCl.
- Concentration of the weak base is 0.220 M.
- Concentration of HCl is also 0.220 M.
- The Kb value for the weak base is 4.0x10^-9.
Step 1: Calculate the moles of the weak base and HCl.
To find the moles, we multiply the concentration (Molarity) by the volume (which is equal for both substances). However, since the volume is not given, it cancels out when calculating the pH. Therefore, we can proceed directly to the next step.
Step 2: Determine the reaction that occurs between the weak base and HCl.
When the weak base reacts with HCl, it forms its conjugate acid and water. The equation is as follows:
Weak base + HCl → Conjugate acid + H2O
Step 3: Write the expression for the Kb (base dissociation constant) of the weak base.
The Kb expression for the weak base can be written as:
Kb = [conjugate acid] [OH-] / [weak base]
Since we started with equal concentrations of the weak base and HCl, we can assume the initial moles of the weak base and the resulting conjugate acid are the same.
Step 4: Use the Kb expression to find [OH-].
The concentration of OH- is equal to the concentration of the conjugate acid because their initial moles are the same (as mentioned in Step 3). Let's represent the concentration of OH- as [OH-] and the weak base concentration as [weak base]:
Kb = [OH-]² / [weak base]
Solving for [OH-]:
[OH-]² = Kb * [weak base]
[OH-] = √(Kb * [weak base])
Step 5: Calculate pOH.
To calculate pOH, we need to take the negative logarithm of [OH-]. The formula is:
pOH = -log10([OH-])
Step 6: Calculate pH using pOH.
To calculate pH, we use the formula:
pH = 14 - pOH
Putting it all together:
1. Calculate [OH-] using the equation derived in Step 4.
2. Calculate pOH using the equation derived in Step 5.
3. Calculate pH using the equation derived in Step 6.
Let me calculate the pH for you.