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QUESTION

# What is the hydroxide ion concentration in a solution of ##"NH"_3## with a ##"pOH"## of ##4.65##?

##["OH"^(-)] = 2.24 * 10^(-5)"M"##

Your starting point here will be the definition of a solution's ##"pOH"##, which as you know is defined as the negative log base ##10## of the concentration of hydroxide anions, ##"OH"^(-)##

##color(blue)(ul(color(black)("pOH" = - log(["OH"^(-)]))))##

Now, in order to solve for the concentration of hydroxide anions, you must rearrange this equation as

##log(["OH"^(-)]) = - "pOH"##

and rewrite it using exponents of base ##10##

##10^log(["OH"^(-)]) = 10^(-"pOH")##

This is equivalent to

##color(blue)(ul(color(black)(["OH"^(-)] = 10^(-"pOH"))))##

Now all you have to do is to plug in the value given to you for the ##"pOH"## of the solution

##["OH"^(-)] = 10^(-4.65) = color(darkgreen)(ul(color(black)(2.24 * 10^(-5)"M")))##

I'll leave the answer rounded to three .