To find the percentage dissociation of HeN in a 0.1 M solution with a given dissociation constant, we follow these steps:
1. Understand the dissociation of HeN:
Let the dissociation of HeN in water be represented by the following chemical equation:
[tex]\[ \text{HeN} \rightleftharpoons \text{He}^+ + \text{N}^- \][/tex]
Here, HeN dissociates into He⁺ and N⁻ ions.
2. Define initial concentration and dissociation constant:
Initial concentration of HeN, [tex]\([ \text{HeN} ]_0 = 0.1 \ M\)[/tex]
Dissociation constant, [tex]\( K_d = 1.8 \times 10^{-5} \)[/tex]
3. Set up the equilibrium expressions:
Let [tex]\( x \)[/tex] be the concentration of HeN that dissociates at equilibrium.
At equilibrium:
[tex]\[ [\text{He}^+] = x \][/tex]
[tex]\[ [\text{N}^-] = x \][/tex]
[tex]\[ [\text{HeN}] = \text{Initial concentration} - \text{Dissociated amount} = 0.1 - x \][/tex]
4. Write the expression for the dissociation constant [tex]\( K_d \)[/tex]:
[tex]\[ K_d = \frac{[\text{He}^+][\text{N}^-]}{[\text{HeN}]} \][/tex]
Substituting the equilibrium concentrations, we get:
[tex]\[ K_d = \frac{x \cdot x}{0.1 - x} = \frac{x^2}{0.1 - x} \][/tex]
5. Solve for [tex]\( x \)[/tex]:
Plug in the given value of [tex]\( K_d = 1.8 \times 10^{-5} \)[/tex]:
[tex]\[ 1.8 \times 10^{-5} = \frac{x^2}{0.1 - x} \][/tex]
6. Solve the quadratic equation:
Rearrange and solve the quadratic equation to find [tex]\( x \)[/tex].
After solving, the positive root gives the concentration of He⁺ (or N⁻) at equilibrium:
[tex]\( x = 0.001332670973077975 \ M \)[/tex]
7. Calculate the percentage dissociation:
Percentage dissociation is calculated using the formula:
[tex]\[ \% \text{dissociation} = \left( \frac{\text{concentration of dissociated HeN}}{\text{initial concentration}} \right) \times 100 \][/tex]
[tex]\[ \% \text{dissociation} = \left( \frac{0.001332670973077975}{0.1} \right) \times 100 \approx 1.33267 \][/tex]
So, the percentage dissociation of HeN in a 0.1 M solution at equilibrium is approximately [tex]\( 1.33 \% \)[/tex].
