Question

If you ever swam in a pool and your eyes began to sting and turn red, you felt the effects of an incorrect pH level. pH measures the concentration of hydronium ions and can be modeled by the function p(t) = −log10t. The variable t represents the amount of hydronium ions; p(t) gives the resulting pH level.

Water at 25 degrees Celsius has a pH of 7. Anything that has a pH less than 7 is called acidic, a pH above 7 is basic, or alkaline. Seawater has a pH just more than 8, whereas lemonade has a pH of approximately 3.

Create a graph of the pH function either by hand or using technology. Loc

Answer 1

Locate on your graph where the pH value is 0 and where it is 1. You may need to zoom in on your graph.

Answer 2

oh hello :)

Answer 3

Hey you!

Answer 4

It had to be math e.e

Answer 5

Yes my worst subject

Answer 6

Why am I here?

Answer 7

Math... I am not sure about this one sorry...

Answer 8

@FortyTheRapper

Answer 9

if it was more understandable for me, I could do it, but like, idek this yet, although, it seems easy but, I haven't learned it yet so I cant help u :( ill tag peeps tho

Answer 10

@Awolflover1 @AloneS @the_ocean_girl @YoungStudier

Answer 11

They have made this a little more confusing than it has to be. Usually we use H+ in chemistry instead of t, but you can also use X, Y if it's easier where Y = -log(X) where X= hydronium and Y = pH.

Which also means Y=p(t) and X = t.

To graph this, I would suggest using values for X like 0.1, 0.2, 0.5, 0.7, 1.0, 1.5, or similar numbers. Then use your calculator to calculate Y values for each of these X values and plot them. You can also use a spreadsheet. If you have Excel I can help you to use it. Either way you can then use your graph to answer the questions in part 1 where Y = 0 and Y=1 and just read off the X values.

Part 2 is worded badly. It's ambiguous to say "raised by 0.5" since if you raise hydronium (= X) by 0.5, the change in pH (=Y) will vary depending on where you start. They meant "raise to 0.5", though they do say this at the end of the question. Anyway, you can easily read it off your graph using 0.5 as the X value.

Now to set up the exponential function this is much easier than it sounds. Just remember that a logarithm is the inverse of an exponent so they cancel each other out: As an example log(10X) = X.

So applying here, just take this equation Y = -log(X) and raise 10 to both sides of the equation:

10Y = 10-log(X) which gives you 10Y = 1/X or more usefully X = 10-Y where again X= hydronium and Y = pH


Part 3, these questions actually have no relationship to anything in chemical reality, but are just exercises to see if you can manipulate the graph and function. But they do illustrate at least one interesting point. Note that in the equation

X = 10-Y

X can never =0. This makes sense since there is nothing you can raise 10 to that will make it zero. It also makes sense chemically since in water you can never have zero hydronium. Similarly using the other form

Y = -log(X)

You know X can also never be zero since you can't have log(0).


Now when they ask for a "Y intercept" they are asking for when X=0 which as stated is never in the above case. However when you transform the equation the ways they want you to, then maybe sometimes you can:

So for p(t) + 1 that really means Y = -log(x) + 1. Still here you can not have a Y intercept (X can't =0) since you would still have log(0) which is forbidden.

But p(t+1) really means Y = -log(X+1). Here of course X can be zero since that just gives you log(1). So you have a Y-intercept.

I'll leave it for you to figure out the third one, the question being if you set X=0, will you get log(0)? If so, that's forbidden. If not, you will have a Y intercept.

Answer 12

Sorry that took a while :P

Answer 13

How did you know the other parts? lol!

Answer 14

I looked it up xD

Answer 15

I still dont get it tho ;-;

Answer 16

What!?!

Answer 17

Idk how to help you :/

Answer 18

first one

Answer 19

okay
we need to plot the graph of this thing-

\(\Large p_H= - log_{10}(t)\)

here t is the hydronium ion concentration

okay
we will graph it using desmos
this is the link to desmos- https://www.desmos.com/calculator

i wrote the equation there
and it graphed it- https://www.desmos.com/calculator/p6o9m0ghsf

so we have completed the 1st part which was to graph that equation

Answer 20

Mkay Im going to make a new post now