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# Definition of pH

## Video transcript

pH is defined as the negative log base 10 of the concentration of hydronium ions so let's say you wanted to find the pH of water so to find the pH of water we would take the negative log of the concentration of hydronium ions and for water at 25 degrees Celsius the concentration is 1.0 times 10 to the negative 7 molar so to find the pH so if you know logarithms you can do this in your head but if you don't I'll get out the calculator here and show you what's do on the calculator you would press negative log of 1.0 times 10 to the negative 7 and we get seven here for our answer so a pH of seven if you're concerned with significant figures you would have to write seven point zero zero and that's because we had two significant figures for our concentrations of one and two and when you're dealing with logarithms the only significant figures in a logarithm are the digits to the right of the decimal point so here's our decimal point and we have two significant figures to the right of our decimal point matching the number we had here so water has a pH of seven and we know that water is neutral let's compare water to two another example let's say we have some orange juice so let's say we're trying to calculate the the pH of our orange juice and I'll just make up a number let's say we measure the hydronium ion concentration to be about 1.5 times 10 to the negative 4 molar so what is the pH of our orange juice solution so the pH is equal to the negative log of the concentration of our hydronium ion which is 1.5 times 10 to the negative 4 so let's get out the calculator and let's do this calculation here so we have negative log of one point five times ten to the negative four so we get we get three point eight two and notice how I'm rounding that so three point eight two if I if I write three point eight two for our answer here that gives us that gives us two significant figures right to the right of our decimal point which is how many we had to account for right here so a pH of three point eight two is lower than seven obviously so whenever your pH is is lower than seven right you're talking about an acidic solution here so our orange juice solution is acidic all right let's uh let's talk about going in Reverse let's say they gave you the pH and asked you for the concentration of hydronium ions so let's say they gave you we'll just use three point eight to just make things a little bit easier so they give you the pH and ask you to solve for the hydronium ion concentration you take the pH is equal to the negative log of the hydronium ion concentration so the negative log of h3o plus and so we can put the negative sign on the left here and so we get negative three point eight two is equal to the log of h3o plus so to solve for the concentration of h3o plus we need to take the antilog right the anti log of the negative ph and that's just ten to the negative three point eight two so let's get out the calculator and let's do let's do ten to the negative three point eight two and that's going to give us one point five one point five because we have to we have to round to one point five here if we're concerned about significant figures times ten to the negative four so let's go ahead and write that one point five times ten to the negative four is the concentration of hydronium ions and so if we get if we get two significant figures here we need two significant figures for our answer and obviously we know this the correct concentration of hydronium ions because it's the same problem as up here right so that's the concentration that we had so if you're trying to find the concentration of hydronium ions you all you need to do is take 10 to the negative pH all right so we found the pH for water and we found the pH for orange juice let's do the pH of ammonia so let's look at this next problem here so calculate the pH of an aqueous ammonia solution with a hydroxide ion concentration of 2.1 times 10 to the negative third molar so they want us to find the pH and pH is equal to negative log of the concentration of hydronium ions but they gave us the concentration of hydroxide ions so we needed we need something that relates h3o plus to o h- and this is the equation we talked about in an earlier video so the concentration of hydronium ions times the concentration of hydroxide ions is equal to kW which is 1.0 times 10 to the negative 14 so if we plug this number in here for the hydroxide ion concentration all right we could say the hydronium ion concentration is X so x times 2 point 1 times 10 to the negative third is equal to 1.0 times 10 to the negative 14 so simple math we solve for X X represents the concentration of hydronium ions so we can get out the calculator and do this calculation here 1.0 times 10 to the negative 14 and we need to divide 2.1 times 10 to the negative third and so we get we get 4.8 times 10 to the negative 12 so I write 4.8 times 10 to the negative 12 which is the molar concentration of hydronium ions here and so we can take this number and plug it into here to calculate the pH so the pH of our solution is equal to a negative log of 4 point H times 10 to the negative 12 so let's look at the calculator and let's let's do this calculation here negative log of 4 point 8 times 10 to the negative 12 and let's think about rounding that so we need to round that to two digits past decimal points so eleven point three two so the pH the pH of our solution is eleven point three two so once again we had two significant figures here so we have two significant figures to the right of our decimal point and so this pH is greater than 7 all right so if your pH is greater than 7 greater than 7 this is like a greater than symbol here you're talking about a basic solution so our ammonia solution is basic alright there's another way to do this problem but first we have to talk about Poh right so pH is equal to a negative log of h3o plus or you could say pH is equal to negative log of h plus so whichever way you want to do it so we're talking about Poh right that's that would be the negative log of Oh H minus so the negative log of the concentration of hydroxide ions so let's calculate the Poh for water so the Poh of water is equal to negative log well at 25 degrees Celsius the concentration of hydroxide ions is also 1.0 times 10 to the negative 7 so the Poh would be equal to 7 right is the same calculation that we did above for the pH of water and once again if you're concerned about significant figures I'll write seven point zero zero all right so the pH of water was 7 and the Poh of water is also seven so the pH of water plus the Poh of water that's 7 plus 7 so that's 14 so that's another equation that you can use when you're doing acid-base calculations here all right so let's do the problem again let's the pH of our ammonia solution again this time using Poh because we're given the concentration of hydroxide to be two point one times 10 to the negative third molar so we could plug that into here and calculate the Poh so let's do that the Poh would be equal to the negative log of let's plug in our concentration to point one times 10 to the negative third so the Poh is equal to let's get out the calculator and do the math so we have negative log of two point one times 10 to the negative third and we get we get two point six eight after we round that so the Poh is two point six eight once again two significant figures here so we put two here so the Poh is two point six eight right we could plug that into here and solve for the pH all right so the pH plus the Poh which is two point six H is equal to 14 and so 14 minus two point six eight gives us eleven point three two which obviously is the same as the same pH that we got when we calculated it a different way so it does not matter how you do it right you're going to get the same answer either way all right let's uh let's look at a let's look at a pH scale here and let's let's put in some of the things we talked about in this video so we talked about water having a pH of seven so water has a pH of seven I'm putting seven right here and we said this was neutral so neutral and this was water next we calculated the pH of an orange juice solution and let's see what we got I don't know what we got for our for our pH here so for our our shoes we got a pH of three point eight two so less than seven so let's go ahead and put that in here so three point a two let's say that's about three point eight two right there so this represents our orange juice solution and when your pH is less than 7 you're talking about an acidic solution so anything anything below 7 you're talking about an acidic solution and then we calculate the pH of our ammonia solution as eleven point three two so let's say that's about eleven point three two here for our ammonia for our ammonia solution and when the pH is greater than 7 right we're talking about a basic solution so to the right of water and we're talking about a base here and normally for your pH scale usually c0 to 14 and most things are probably going to fall between 0 and 14 but it's possible to have for example a pH less than zero right it just depends on what your concentration of hydronium is and so that's the idea of a pH scale right looking at things compared compared to compared to water thinking about if a solution is acidic or basic