Question

The value of Ka for nitrous acid (HNO2) at 25 ∘C is 4.5×10−4 .a. Write the chemical equation for the equilibrium that corresponds to Ka1. H+(aq)+NO−2(aq)⇌HNO2(aq)2. HNO2(aq)⇌H+(aq)+NO−2(aq)3. HNO2(aq)⇌H−(aq)+NO+2(aq)4. HNO2(aq)+H+(aq)⇌H2NO+2(aq)5. HNO2(aq)+H−(aq)⇌H2NO+2(aq)​b. By using the value of Ka , calculate ΔG∘ for the dissociation of nitrous acid in aqueous solution. c. What is the value of ΔG at equilibrium? d. What is the value of ΔG when [H+] = 5.9×10−2 M , [NO−2] = 6.7×10−4 M , and [HNO2] = 0.21 M ?

Answer 1

Answers and Explanation:

a)- The chemical equation for the corresponden equilibrium of Ka1 is:

2. HNO2(aq)⇌H+(aq)+NO−2

Because Ka1 correspond to a dissociation equilibrium. Nitrous acid (HNO₂) losses a proton (H⁺) and gives the monovalent anion NO₂⁻.

b)- The relation between Ka and the free energy change (ΔG) is given by the following equation:

ΔG= ΔGº + RT ln Q

Where T is the temperature (T= 25ºc= 298 K) and R is the gases constant (8.314 J/K.mol)

At the equilibrium: ΔG=0 and Q= Ka. So, we can calculate ΔGº by introducing the value of Ka:

⇒ 0 = ΔGº + RT ln Ka

   ΔGº= - RT ln Ka

   ΔGº= -8.314 J/K.mol x 298 K x ln (4.5 10⁻⁴)

  ΔGº= 19092.8 J/mol

c)- According to the previous demonstation, at equilibrium ΔG= 0.

d)- In a non-equilibrium condition, we have Q which is calculated with the concentrations of products and reactions in a non equilibrium state:

ΔG= ΔGº + RT ln Q

Q= ((H⁺) (NO₂⁻))/(HNO₂)

Q= ( (5.9 10⁻² M) x (6.7 10⁻⁴ M) ) / (0.21 M)

Q= 1.88 10⁻⁴

We know that   ΔGº= 19092.8 J/mol, so:

ΔG= ΔGº + RT ln Q

ΔG= 19092.8 J/mol + (8.314 J/K.mol x 298 K x ln (1.88 10⁻⁴)

ΔG= -2162.4 J/mol

Notice that ΔG<0, so the process is spontaneous in that direction.

Answer 2

HNO2 is a weak acid whose dissociation occurs as follows;  HNO2 (aq)    ⇋       H+ (aq)  +      NO2- (aq)

The equation for the dissociation of HNO2 is;

           HNO2 (aq)    ⇋       H+ (aq)  +      NO2- (aq)

We can use the value of Ka to find the  ΔG∘ for the dissociation of nitrous acid in aqueous solution as follows;

ΔG∘ = -RTlnKa

Where;

R = Gas constant = 8.314 J/K. mol

Ka = Acid dissociation constant = 4.5×10^−4

T = temperature = 25 ∘C or 298 K

Substituting values;

ΔG∘ = -(8.314 J/K. mol × 298 K × ln 4.5×10^−4)

ΔG∘ = 19.1 KJ/mol

Given that;

Q = [ H+] [NO2- ]/[HNO2]

[ H+] =  5.9×10−2 M

[NO2- ] = 6.7×10−4 M

[HNO2] = 0.21 M

Q = [5.9×10−2 M] [6.7×10−4 M]/[0.21 M]

Q = 1.88 × 10^−4

From the formula;

ΔG = ΔG∘ + RTlnQ

ΔG =  19.1  KJ/mol + (8.314 J/K. mol  ×  298 K ×  ln 1.88 × 10^−4)

ΔG = -2.15 KJ/mol

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