How many grams of pure NaOH must be used to prepare 10.0 L of a solution that has a pH of 13?

Question

joannablackwelder · Answer

pH=-log[H+]

joannablackwelder · Answer

1.0x10^-14=[H+][OH-]

joannablackwelder · Answer

M=mol/L

joannablackwelder · Answer

Any ideas on how to use these formulas for this problem?

rushwr · Answer

Hey ,
The 1st thing to pop  when u read this question is that we can't do anything with pH since it is a base. So u have to find a way to get the pOH from pH for that we can use the following, $$14 =pH+pOH$$ 
(since they haven't given us any detail about the temp and pressure, we will take it at stp so )
Now we found that pOH is equal to 14-13= 1

rushwr · Answer

Now we can find the concentration of OH 
using $$pOH = -\log_{10}[OH ^{-}]$$
So will be getting an answer around 0.1 moldm-3
So now we know the concentration of OH- and we also know the volume of of it which 10L 
Now using $$C * V= n$$ find the no. of moles (n), which will be 1mol
We know the no. of moles of OH- is equal to the no. of moles of NaOH
Now using $$n=\frac{ m }{ M _{w} }$$ find the mass (m). As we know the r.m.m. of NaOH which is 40gmol-1
So the mass of NaOH will be 1mol x 40gmol-1 which is equal to 40gmole again ! simple right? HOpe u got it