Question #df7ec

1 Answer
Oct 17, 2016

Answer:

#"pH" = 1.60#

Explanation:

The pH of a solution is simply a measure of the concentration of hydrogen ions, #"H"^(+)#, which are sometimes called hydronium ions, #"H"_3"O"^(+)#.

More specifically, the pH of a solution is defined as

#color(blue)(bar(ul(|color(white)(a/a)"pH" = - log(["H"^(+)])color(white)(a/a)|)))#

Here #["H"^(+)]# represents the molarity, or molar concentration, of the hydrogen ions.

This means that all you have to do to find the solution's pH is take the negative log base #10# of the concentration of hydrogen ions.

In your case, this will get you

#"pH" = - log(2.5 * 10^(-2))#

Now, you can use the properties of the log function to say that

#"pH" = - [log(2.5) + log(10^(-2))]#

which gets you

#"pH" = - [log(2.5) + (-2) log10]#

#"pH" = - [log(2.5) - 2]#

#"pH" = 2 - log(2.5)#

You can say for sure that the pH of this solution is lower than #2#. You can play around with this even more to find

#"pH" = 2 - log(10/4)#

#"pH" = 2 - (log10 - log4)#

#"pH" = 2 - 1 + log4#

#"pH" = 1 + log4#

You can now say that the pH is higher than #1#. Finally, you can use a calculator to get the exact value

#color(green)(bar(ul(|color(white)(a/a)color(black)("pH" = 1 + log4 = 1.60)color(white)(a/a)|)))#