Question

Nitrous acid, HNO2, has a Ka of 7.1 x 10-4. What are (H3O+), (NO2-), and (OH-) in 0.700M HNO2?

a)   (H3O+)=.........M…………………………answer a in M

b))   (NO2-)=..........M…………………………answer b in M

c)   (OH-)..............x 10 .......M...........( answer c   in scientific notation)

Answer 1

a)
HNO2 dissociates as:

HNO2          ----->     H+   + NO2-
0.7                 0         0
0.7-x               x         x


Ka = [H+][NO2-]/[HNO2]
Ka = x*x/(c-x)
Assuming x can be ignored as compared to c
So, above expression becomes

Ka = x*x/(c)
so, x = sqrt (Ka*c)
x = sqrt ((7.1*10^-4)*0.7) = 2.229*10^-2

since x is comparable c, our assumption is not correct
we need to solve this using Quadratic equation
Ka = x*x/(c-x)
7.1*10^-4 = x^2/(0.7-x)
4.97*10^-4 - 7.1*10^-4 *x = x^2
x^2 + 7.1*10^-4 *x-4.97*10^-4 = 0
This is quadratic equation (ax^2+bx+c=0)
a = 1
b = 7.1*10^-4
c = -4.97*10^-4

Roots can be found by
x = {-b + sqrt(b^2-4*a*c)}/2a
x = {-b - sqrt(b^2-4*a*c)}/2a

b^2-4*a*c = 1.989*10^-3

roots are :
x = 2.194*10^-2 and x = -2.265*10^-2

since x can't be negative, the possible value of x is
x = 2.194*10^-2

So, [H+] = x = 2.194*10^-2 M
Answer: 0.0219 M

b)
[NO2-] = x = 2.194*10^-2 M
Answer: 0.0219 M

c)
Given:
[H+] = 2.194*10^-2 M

use:
[OH-] = Kw/[H+]
Kw is dissociation constant of water whose value is 1.0*10^-14 at 25 oC
[OH-] = (1.0*10^-14)/[H+]
[OH-] = (1.0*10^-14)/(2.194*10^-2)
[OH-] = 4.558*10^-13 M
Answer: 4.56*10^-13 M