As the feedback and solution both indicate, the difference in calculate #"pH"# once solving through the quadratic equation and also the presumption that #x# is little enough different by only #0.01# #"pH"# units, so making use of the #x#-is-small presumption is recommended.

#K_a = 1.8 * 10^(–4)# in ~ #25^


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Formic mountain is a weak acid, therefore you know that the will just partially ionize in aqueous systems to create formate anions and also hydronium cations.

#"HCOOH"_ ((aq)) + "H"_ 2"O"_ ((l)) rightleftharpoons "HCOO"_ ((aq))^(-) + "H"_ 3"O"_ ((aq))^(+)#

Notice that every #1# mole that formic acid that ionizes produces #1# mole of formate anions and #1# mole of hydronium cations.

Now, let"s say the #x# #"M"# is the concentration the formic acid that ionizes. Because formic mountain is a weak acid, you understand for a truth that

#x quad "M"

In various other words, only a fraction of the early concentration that the acid will certainly actually ionize. Follow to the balanced chemical equation, the solution will save

#<"HCOO"^(-)> = <"H"_ 3"O"^(+)> = x quad "M"#

When #x# #"M"# that formic mountain ionizes, you acquire #x# #"M"# the formate anions and also #x# #"M"# that hydronium cations.

So at equilibrium, you have the right to express the concentration the the formate anions and the concentration the the hydronium cations in regards to the concentration that formic mountain that ionizes. At equilibrium, the resulting solution will also contain

#<"HCOOH"> = (0.0700 - x) quad "M"#

When #x# #"M"# the formic acid ionizes, the early concentration the the acid decreases through #x# #"M"#.

See more: Which One Of The Following Compounds Contains Ionic Bonds? ?

By definition, the acid dissociation constant that explains the ionization equilibrium of formic acid is equal to

#K_a = (<"HCOO"^(-)> * <"H"_ 3"O"^(+)>)/(<"HCOOH">)#

In your case, this will be same to

#K_a = (x * x)/(0.0700 - x)#

which is

#1.8 * 10^(-4) = x^2/(0.0700 - x)#

Now, you understand that making use of the approximation

#0.0700 - x ~~ 0.0700#

is encourage here, for this reason rewrite the expression of the mountain dissociation consistent as

# 1.8 * 10^(-4) = x^2/0.0700#

This will obtain you

#x = sqrt(0.0700 * 1.8 * 10^(-4)) = 0.003550#

Since #x# to represent the equilibrium concentration that hydronium cations, you have the right to say the the solution will have

#<"H"- 3"O"^(+)> = "0.003550 M"#

As girlfriend know, the #"pH"# that the equipment is offered by

#"pH" = - log in (<"H"_3"O"^(+)>)#

Plug in your worth to find

#"pH" = - log(0.003550) = color(darkgreen)(ul(color(black)(2.450)))#

The price is rounded to 3 decimal places since you have three sig figs for the early concentration the formic acid.