Acids and bases
pH of a Weak Base pH of .2 M of NH3 (weak base).
pH of a Weak Base
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- We've dealt with the weak acid, so let's try an example
- with the weak base.
- Let's say we had ammonia.
- That's nitrogen with three hydrogens.
- And it's a weak base because it likes to accept hydrogen
- from water, leaving the water with just a hydroxide.
- So it increases the hydroxide concentration.
- So if you have some ammonia in an aqueous
- solution, plus water.
- I'll throw the water in there.
- Plus water in an aqueous solution.
- It's a weak base.
- So this reaction doesn't go in just one direction.
- It's an equilibrium reaction.
- And since this is a weak base, it-- and this is where the
- Bronsted-Lowry definition really kind of pops out.
- Is that it's a proton acceptor instead of a donor.
- So it turns into ammonium, or an ammonia cation.
- Ammonium has another hydrogen on it, so now
- it has another proton.
- So it's the plus charge.
- An it's an aqueous.
- And it took that hydrogen from the water.
- So plus OH minus aqueous.
- And remember, if you look at it from the Bronsted-Lowry
- definition , it was a proton acceptor.
- So that made it a base.
- Or if you look at the Arrhenius definition, it
- increased the concentration of OH in the solution, so that
- makes it an Arrhenius base.
- But anyway, given that we have-- let me
- pick a random number.
- Let's say we have 0.2 molar of NH3.
- What is going to be the pH?
- So what's going to be our pH of the solution, considering
- that it's 0.2 molar of NH3.
- So the first thing we need to do.
- We need to figure out the equilibrium constant for this
- base reaction.
- And I just went to Wikipedia-- I wanted to say liquidpedia,
- I'm talking about liquids so much.
- And equilibrium.
- But I went to Wikipedia, and they have a little chart for
- almost any compound you look for.
- And they give you pKb.
- Which is, you see that p there.
- That just means it's the minus log base 10 of
- the equilibrium constant.
- And they give that as being 4.75.
- So we can just do a little bit of math here to solve for the
- equilibrium constant.
- So let's see.
- If we multiply both sides by negative, you get log base 10
- of our equilibrium constant for this base reaction.
- That's why the b is there.
- Is equal to minus 4.75, or 10 to the minus
- 4.75 should be Kb.
- So Kb is equal to 10 to the minus 4.75.
- That's not an easy exponent to figure out in your head, so
- I'll bring out the calculator for that.
- So if we take 10 to the 4.75 minus, it equals, let's just
- say 1.8 times 10 to the negative 5.
- This is equal to 1.8 times 10 to the minus 5.
- So now we can use this information and we can do a
- mathematical thing very similar to we
- did in the last video.
- It's going to be hard to figure out the hydrogen
- concentration directly, right?
- Because our equilibrium reaction only has hydroxide.
- But if we know the hydroxide concentration, then we can
- back into the hydrogen concentration, knowing that
- this plus the hydrogen concentration has to equal 10
- to the minus 14.
- Or if you figure out the pOH, that plus the pH has to be 14.
- And we did that a couple of videos ago.
- So this equilibrium constant or this formula
- would look like this.
- 1.8 times 10 to the minus 5 will be equal to-- in the
- denominator, we have our concentration of reactants.
- And remember, you don't include the solvent.
- So you only include the NH3.
- We have 0.2 molars is what we put in, but some of it, let's
- say X of it, is going to be converted into this stuff on
- the right-hand side.
- So in the denominator, we're going to have 0.2 minus
- whatever gets converted into the right-hand side.
- And so then in the right-hand side, we're going to have x of
- NH4 and x of OH.
- This is the concentration of ammonia.
- And then we have x times x.
- This is the concentration of NH4 plus-- that's a 4.
- And then this is the concentration,
- right here, of OH minus.
- And we just solve for x.
- Let's do that.
- Solve for x.
- And once we have x, we know the concentration of OH.
- We'll be able to figure out the pOH, and then we'll be
- able to figure out the pH.
- Multiply this times both sides of this equation.
- And just so you know, that same simplification step that
- we did in the previous thing.
- When this is several orders of magnitude smaller than this
- number right here-- I want to give you-- heuristics are just
- kind of rules of thumb that sometimes work.
- Let's just do the quadratic equation.
- But you can kind of think about sometimes when you can
- get rid of that middle term.
- But let's just multiply it.
- 0.2 two times 1.8 is 0.36.
- 0.36 times 10 to the minus 5, right?
- 2 times 1.8 would be 3.6, this is 0.36.
- Minus 1.8 times 10 to the minus 5 x, right?
- Is equal to that.
- x squared.
- Let's put everything on the same side of the equation.
- I'm going to move all of these the right-hand side, so you
- get 0 is equal to x squared.
- Add this to both sides of the equation.
- Plus 1.8 times 10 to the minus 5 x.
- 1.8 times 10 to the minus 5.
- Just so you can see the coefficients separate from the
- x terms.
- Minus 0.36 times 10 to the minus 5.
- So let's solve this.
- And once again, if you wanted to kind of do it, you could
- eliminate this term and then just figure out the straight
- up square root.
- But we won't do that.
- We'll actually use a quadratic equation.
- So a is 1.
- b is this.
- That's b.
- And this is c.
- And you just supply than in the quadratic equation.
- So you get minus b.
- So you minus 1.8 times 10 to the minus 5 power.
- Plus or minus.
- We'll only have to do the plus because if we do the minus,
- we'll end up with a negative concentration.
- So plus, the square root-- we have to do a lot of math
- here-- b squared.
- So it's 1.8 times 10 to the negative 5.
- So it's 1.8.
- If you square it, it's 3.24.
- So it's 3.24 times-- if you square 10 to the minus 5-- 10
- to the minus 10 minus 4 times a, which is 1,
- times c, which is minus.
- So it's 4 times-- the minuses cancel out-- times 0.36 times
- 10 to the minus 5.
- Which is 4 times 0.36 is equal to 1.44.
- I should have been able to do that in my head.
- Now you have 1.44 e minus 5.
- Times 10 to-- let me write that.
- So this is 1.44.
- And of course all of this is over 2a.
- So let's see.
- This is my x value.
- My concentration of OH.
- So let's see.
- I have 3.24 times 10 to the minus 10.
- That's that.
- Plus 1.44 times 10 to the minus 5 is equal to that.
- So that's this whole thing under the radical.
- And I want to take the square root of that.
- And so that is to the 0.5 power.
- So I get 0.00379.
- So I'll switch colors.
- So I get x is equal to a minus 1.8 times 10 to the minus 5
- plus 0.003794.
- All of that over 2.
- Do the math.
- So to that I'm going to subtract minus this point
- right here.
- I have this value.
- I'm just subtracting this.
- Minus 1.8 e 5 negative is equal to that.
- This is the whole numerator.
- And now I need to just divide it by 2.
- Divided by 2 is equal to 0.001.
- Let me write that.
- So x.
- So I'll switch colors arbitrarily again.
- x is equal to 0.001888-- I mean, then there's a 3 and so
- forth and so on.
- But if you remember from our original equation.
- What was x?
- It was what's both the ammonium concentration and the
- hydroxide concentration.
- We care about the hydroxide concentration.
- So this is equal to my concentration of hydroxide.
- Now if I want to figure out my pOH, I just take the minus log
- of this number, which is equal to--
- So let's just take the log of it.
- The log is that, and then I take the minus of that.
- So it's 2.72.
- And now if we want to figure out the pH, my concentration
- of hydrogen ions-- just remember, when you're in an
- aqueous solution at 25 degrees Celsius, your pK of water is
- equal to your pOH plus your pH.
- This at 25 degrees is 14.
- Because you have 10 to the minus 14 molar concentration--
- well no, actually, I don't want to go into that.
- You have 10 to the minus 7 of each of these.
- But anyway, this is equilibrium constant for the
- disassociation of water.
- This, when water's neutral is 7 or a concentration of OH of
- 10 to the minus 7.
- We can take the minus log, this becomes 7.
- But now we know we have a much higher concentration of OH.
- Remember, that minus log kind of flips it.
- So a lower pOH means a higher concentration of pOH.
- And a lower pOH, if this is lower, right?
- This is a lower pOH.
- That means your pH is higher.
- So what is your pH going to be?
- So your pH is going to be equal to 14 minus 2.72.
- So let me do the minus plus 14 is equal to--
- let's just say 11.3.
- So your pH is equal to 11.3.
- Which makes sense, because we said this was a weak base.
- Ammonia is a weak base.
- So it's basic.
- So it should increase your pH above the neutral 7.
- So the pH should be greater than 7, but as you compare it
- to some of the strong bases before that took our pH when
- you added a molar to 14, this took our pH-- although we only
- did add 0.2 molar of it to 11.3.
- Anyway, this is more of a math problem than chemistry, but
- hopefully it clarified a few things as well.
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