Use the information below to answer the following question. What is the pH of a 0.100 M solution of benzoic acid?

Use the information below to answer the following question. What is
the pH of a 0.100 M solution of benzoic acid?
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1 Answer
Sep 8, 2016

Answer:

#pH# #=# #-log_10(2.5xx10^-3)# #=# #2.60#

Explanation:

Benzoic acid is a weak acid, whose dissociation we represent as:

#C_6H_5CO_2H(aq) +H_2O(l) rightleftharpoonsC_6H_5CO_2^(-) + H_3O^+#

Using the usual conventions, #K_a=([H_3O^+][C_6H_5CO_2^(-)])/([C_6H_5CO_2H])#

#K_a=6.3xx10^-5# #=# #(x^2)/(0.100-x)#

Where #x# #=# #[H_3O^+]=[C_6H_5CO_2^(-)]#

We have a quadratic in #x#, that in principle we could solve directly. I'm not gonna cos I'm lazy. If we say #(0.100-x)~=0.100#, then #x# #=# #sqrt{6.3xx10^(-5)xx0.100}# #=# #2.5xx10^-3#.

I am not going to bother to do another approx. but perhaps you should; i.e. plug your first approx. back into the equation to see how the answer evolves.

#x=[H_3O^+]# #=# #2.5xx10^-3*mol*L^-1#

And #pH# #=# #-log_10(2.5xx10^-3)# #=# #2.60#