Question #0059f

As you know, the #"pH"# of a solution is calculated by taking the negative log base #10# of the concentration of hydrogen ions, #"H"^(+)#, which you'll sometimes see referred to as hydronium ions, #"H"_3"O"^(+)#

#"pH" = - log_10(["H"^(+)])#

or, more simply

#"pH" = - log(["H"^(+)])#

In your case, the #"pH"# of the solution is equal to #9.7#. Right from the start, the fact that you have

#"pH" > 7#

tells you that you're dealing with a basic solution, which, at room temperature, is a classification given to any solution that has

#["H"^(+)] < 10^(-7)# #"M"#

To find the actual concentration of hydrogen ions, rewrite the equation as

#log(["H"^(+)]) = - 9.7#

Now use both sides as exponents for #10# to say that

#10^log(["H"^(+)]) = 10^(-9.7)#

By definition, you have

#a^(log_ax) = x" "(AA)color(white)(.) a>0, x>0, a, x in RR#

This means that

#10^log(["H"^(+)]) = ["H"^(+)]#

which gets you

#["H"^(+)] = 10^(-9.7)#

#["H"^(+)] = 2.0 * 10^(-10)# #"M"#

As predicted, the concentration of hydrogen ions is #< 10^(-7)# #"M"#, which is what you should expect to see for a basic solution.