Answer:
Ka = 1.39x10⁻⁶
Explanation:
A monoprotic acid, HX, will be in equilibrium in an aqueous medium such as:
HX(aq) ⇄ H⁺(aq) + X⁻(aq)
<em>Where Ka is:</em>
Ka = [H⁺] [X⁻] / [HX]
<em>Where [] is the molar concentration in equilibrium of each specie.
</em>
The equilibrium is reached when some HX reacts producing H+ and X-, that is:
[HX] = 1.64M - X
[H⁺] = X
[X⁻] = X
As pH is 2.82 = -log [H⁺]:
[H⁺] = 1.51x10⁻³M:
[HX] = 1.64M - 1.51x10⁻³M = 1.638M
[H⁺] = 1.51x10⁻³M
[X⁻] = 1.51x10⁻³M
And Ka is:
Ka = [1.51x10⁻³M] [1.51x10⁻³M] / [1.638M]
<h3>Ka = 1.39x10⁻⁶</h3>
1 pm = 10∧-10 cm
Therefore, 230 pm is equivalent to 2.3 ×10∧-8 cm.
Atom is in the shape of a sphere,
The volume of a sphere is given by 4/3πr³
Thus, volume of the atom = 4/3π( 2.3 ×10∧-8)³
= 4/3 (3.142 ×12.167×10∧-24
= 5.096 ×10∧-23 cm³
but 1m³= 1000000cm³
Therefore, the volume of the atom = 5.096 ×10∧-29 m³
PH = -log [H3O+]
4.15 = -log [H3O+]
[H3O+] = 10^(-4.15)
[H3O+]= 7.08 × 10^-5