Complete the table. (All solutions are at 25 °C.)

Video transcript

Hey everyone today, we're giving a pretty fun problem to do. So we're asked to consider the following solutions at 25°C. And to fill out the missing information in the table. So let's take a look at the very first line. Were given a hydro name, ion concentration of 8.6 times 10 to the -10. So right off the bat. The easiest thing to do is find the ph the ph which remember is just the negative log of the hydro Nehemiah in concentration. So subbing that in we get that it is a negative log Of 8.6 times 10 to the -10. Which leaves us with a final value of 9. 9.07. Let me write that answer In red because 9. Is above the ph of seven which means that this is basic. However, we're still missing the hydroxide concentration or the yeah hydroxide concentration. And to do this we have to use another identity. So the ionization constant of water organization constant, sorry, is equal to the product of the hydro ni um and hydroxide iron concentrations and the ionization constant is equal to one oops. And the K. W is also equal to 1.0 times 10 to the -14, which means the O H concentration is equal to 1.0 times 10 to the negative 14th divided by 8.6 times 10 to the negative 10 which gives us a value of 1.2 times 10 to the negative fifth. So this will be 1.2 times 10 to the -5. Let me just write that in red for the sake of consistency. two times 10 to the -5. That's the first problem. Taking a look at the 2nd row were given the ph So that means we need to work backwards to find the hydro ni um concentration first because that's the easiest to work with. So if ph is equal to the negative log of concentration as we wrote up here, then that must mean thanks to longer than rules that the hydrogen ion concentration is therefore equal to tend to the power of the negative ph. So substituting in our ph which is 10.8, The 10 to the power of negative 10. we get I had drawn in my own concentration of two times 10 To the -11. So two times 10 to the negative 11th. And because of the Ph is well over seven, it is also basic. Finally again to find our oh h concentration and hydroxide concentration, we can use the same identity that we used here. So the hydroxide concentration will be equal to 1.0 times 10 to the negative 14th divided by the hydrogen ion concentration we just found, which is two times 10 to the negative 11th. And that will give us a value of six times 10 to the negative fourth. Keep in mind that the hydroxide concentration here is far greater. Then the hydrogen ion concentration which only helps solidify the fact that this solution isn't he? Basic. There's a higher concentration of hydroxide ions compared to hydro nia. Moving on row three were given the hydroxide ions only. So what I like to do first is solve for the hydro nima and concentration. We can again use the same KW identity but rearrange it instead to solve for the hydrogen ion concentration. So let me write this in blue here, hydrogen in mind concentration will equal the KW divided by the hydroxide ion concentration. So that'll be 1.0 times 10 to the negative 14th, Divided by 3.8 times 10 to the -10. And that gives us a value of 2.6 Times to the -5. 2.6 times 10 to the -5. And using that, we can go ahead and solve the P. H. So the ph is equal to the negative log of the hydro Nehemiah in concentration. He's 30 plus which is equal to negative log of 2.6 times 10 to the -5, which gives us a final ph Of 4.58. This is well below seven. So that means we're dealing with in acidic solution. Finally, for question # four. Again, the ph is 4.26. So it's well below seven which is neutral ph meaning that this solution is acidic. We can go ahead and use the ph identity. Let's use a different color, Let's use green. We can use the ph identity since P. H. Is equal to the negative logarithms of the hydrogen ion concentration. And the concentration of hydrogen ions must therefore be equal to tend to the negative ph So using our value for P. H. which is 4.26 10 to the negative 4. is equal to 5. Times 10 to the -5. And we can use the kW identity once more to go ahead and solve for the hydroxide concentration. 5.5 times 10 to the -5. So the hydroxide ion concentration will be equal to K. W. Divided by the concentration O H minus. Sorry. Which will give us 1.0 times 10 to the native 14th, divided by oh sorry my bad. We're solving for the hydroxide ion concentration. Not hydro ni. Um But it follows the same rule. The hydroxide ion concentration equal kw divided by hydro name ions. And that will give us 1.0 times 10 to the negative 14 divided by 5.5 times 10 to the negative fifth. Which will give us a final value of 1.8 times 10 to the negative 10th 0.8 Times 10 to the -10. I hope this helps. And I look forward to seeing you on the next one