please show work! Amazonian ants nesting on tree species Duroia hirsuta have bee

Question

please show work!

Amazonian ants nesting on tree species Duroia hirsuta have been reported to inject a lethal dose of formic acid into leaves of other tree species in the vicinity."* In other words, the ants kill off any foliage that might be competitive to their nesting plant. How many milligrams of formic acid, HCOOH, (Mm = 46 g/mol), are required to make 0.575 mL of aqueous solution having a pH of 2.98? The pK for formic acid is 3.74. Treat formic acid like a generic weak acid: HA + H2O = A- + H3O+ Mass formic acid: (mg)

Explanation / Answer

Given pH= 2.98

we know that pH= -log(H30+)

so 2.98 = -log(H30+)

log(H3O+) = -2.98

(H30+)= 1.047 x 10-3

Reaction for given question is

HCOOH + H2O = HCOO- + H3O+

Ka= (HCOO-) (H30+)/(HCOOH)

given pKa= 3.74

-log Ka= 3.74

ka= 1.819 x 10-4

let us assume that we started with a M HCOOH

initial conc of HCOOH, HCOO- ,H3O+ are a,0,0

final conc are a-x,x,x

we got x= 1.047 x 10-3

so Ka= (HCOO-) (H30+)/(HCOOH)

1.819*10-4= (1.047 *10-3)2/a-x

a-x= 0.60 * 10-2

a= 0.60 *10-2 + 1.047 *10-3

a=0.7047 x 10-2 M

Molarity= mass x 1000/ M.w x V (ml)

given M.w = 46 g

V=0.575 ml

mass= molarity x m.w x v/1000

=0.704 x 10-2 x 46 x 0.575/1000

=0.186 x 10-3 g

mass of HCOOH required =0.186 milligram

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