HNO2 is weak acid with Ka of 4.0x10^-4. Determine the H3O+ ion concentration and

Question

HNO2 is weak acid with Ka of 4.0x10^-4. Determine the H3O+ ion concentration and pH of a solution of 0.0030M HNO2. The "x is small" approximation is not valid, so the short cut cannot be used and a solution to a quadratic equation will be required. Show all 6 steps. When finished, fill in these terms for your solution of the quadratic.

a=_____ b=_____ c=_____ x=_____ [H3O+]=_____ pH=_____

steps 1,2,3 (ICE Table)

step 4 approx.

step 4a quadratic (fill in a,b,c aabove)

step 5 [H3O+] and pH

step 6 check

Explanation / Answer

Construct the ICE table

lets write the equation

HNO2 + H2O <---> NO2- + H3O+

I 0.003 0 0

C -x +x +x

E 0.003-x +x +x

now if you write the Ka expression

Ka = [NO2-[H3O+] / [HNO2] Ka is given as a 4.0x10-4

4.0x10-4 = [x][x] / [0.003-x]

x2 + x4.0*10-4 - 1.2 * 10-6 = 0

this is the quadratic equation here

a = 1 , b = 4.0*10-4, c = 1.2 * 10-6

solve the quadratic equation

x = 0.000914

from the ICE table

x is the equilibrium concentration of NO2- and H3O+ so

[H3O+] = 0.000914

pH = -log(H3O+)

pH = -log(0.000914) = 3.04

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