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## AP®︎/College Chemistry

### Course: AP®︎/College Chemistry>Unit 8

Lesson 1: Introduction to acids and bases

# The pH scale

The pH scale is a convenient way to represent the acidity or basicity of a solution. We can calculate the pH of a solution by taking the negative logarithm of the hydronium ion concentration, or pH = -log[H₃O⁺]. At 25°C, a solution with pH < 7 is acidic, a solution with pH > 7 is basic, and a solution with pH = 7 is neutral. Created by Jay.

## Want to join the conversation?

• This might sound extremely stupid, but is there such thing as imaginary pH? We know that the log of something negative is imaginary, and it seems to me that according to E=mc^2, a sufficiently negative amount of potential energy can result in a negative mass. Dividing this negative mass by the molar mass gives us a negative amount of moles, resulting in an imaginary pH. • how does x equal 5.0x10-12? • wait if the conc of 0H- and H30+ are diff, then why can you interchangeably plug in -log[H30+] and -log[0H-]? you get diff answers • If we are looking for the ph of [OH], why did we use the equation pH= -log[H30] and use that value for the ph of OH?
(1 vote) • The video was asking for the pH of a solution which contained both hydronium, H3O^(+), and hydroxide, OH^(-), ions. Aqueous solutions, even very acidic or basic, have both of those ions present at all times, but in different amounts. We can relate the concentration of hydroxide to hydronium through the autoionization of water reaction.

H2O(l) + H2O(l) → H3O^(+)(aq) + OH^(-)(aq)
Where the equilibrium expression, Kw, is: Kw = [H3O^(+)][OH^(-)], and Kw is equal to 1.0x10^(-14) at 25°C.

So if we know the hydroxide concentration then we can solve for the hydronium concentration. If [OH^(-)] is 2.0x10^(-3) M then Kw = [H3O^(+)][OH^(-)] becomes:

1.0x10^(-14) = (2.0x10^(-3))*x, where x is the hydronium concentration, [H3O^(+)]. Dividing both sides by 2.0x10^(-3) means x is 5.0x10^(-12) M.

Now we can use the equation pH = -log([H3O^(+)]) to solve for the pH.

Hope that helps.
(1 vote)
• I've been trying to understand logs for a long time and it's always confusing to me so sorry if this is a simple question. at minutes you took the negative log of hydronium to get 3.44. If I do this in my calculator without the negative sign at the beginning of the log I then get -3.44. If I do it with the negative sign then I get the same answer as you did. Can you explain the underlying concept of this? Am I correct in saying that this is a log law at work here?

I just don't seem to understand the negative sign in front of the log. Thanks in advance!
(1 vote) • sorry if it is a stupid question, but why do we still use water's Kw of 1.0 x 10^(-14) when we're measuring pH of something that's not water/pure water? 