alevel chemistry question

0 Sodium hydrogensulfate is a widely used acid, with applications that include
removing limescale and as a food additive. Sodium hydrogensulfate is a weak acid
because of the presence of the hydrogensulfate ion, HSO4
− .
(a) (i) Write the equation for the dissociation of the hydrogensulfate ion in
aqueous solution. State symbols are not required.
ans:-HSO4− ⇌H+ + SO4 2−

aii) A solution of sodium hydrogensulfate has pH = 1.13
Calculate the concentration of this solution, in g dm−3.
[pKa of HSO4−= 1.92

ansExample of calculation:
Ka = h+^2/[hso4-]
Ka = 10−1.92 (= 0.012023) and [H+] = 10−1.13 (= 0.074131)
[HSO4−] = 0.45709 (mol dm−3)*
Mr(NaHSO4) = 120.1
[NaHSO4] = 120.1 x 0.45709
= 54.896(g dm−3))

can anyone tell me how part aii) makes sense ,from my understanding as nahso4 is a weak acid the concentration of nahso4 cannot equal that of hso4- because of partial dissociation ,then how is it that we calculate the concentration of hso4- and use it as a concentration of nahso4 ?thanks

You are misunderstanding the meaning of dissociation.
The sodium hydrogen sulfate is not dissociating, it is ionic, it is the hydrogensulfate ions that are dissociating.

HSO₄^- <==> H⁺ + SO₄^2-

the ka value for the dissociation is 10^-1.92 = 0.0120

If the hydrogen ion concentration is 10^-1.13 = 0.0741 mol dm^-3

Then as ka = [H+][A-]/[HA]

and [H+] = [A-]

so 0.0120 = (0.0741)²/[HA]

Hence [HA] = 0.458 mol dm^-3

As the ionic compound dissociates 100% this is also the concentration of the sodium hydrogensulfate.

In g dm^-3 = 0.458 x Mr = 0.458 x 120.1 = 55 g dm^-3

oh what i thought was that nahso4 dissociates to give hso4- AND Na+ and was confused how nahso4 can equal hso4- when it partially dissociates to form hso4- as its mentioned that nahso4 is a weak acid .

Remember that all ionic compounds dissociate 100% in solution.
The fact that sodium hydrogensulfate is ionic means that it first dissociates 100% to give:

NaHSO₄ + (aq) <==> Na⁺(aq) + HSO₄^-(aq)

and THEN the weak acid dissociates:

HSO₄^-(aq) <==> H⁺(aq) + SO₄^2-(aq)

You are given ka for this second equation.