We know,
$$-\triangle G^{\circ} = 2.303\ RT \log K_{p}$$
$$-(-16.5\times 10^{3}) = 2.303\times 8.314\times 298\log K_{p}$$
$$\log K_{p} = \dfrac {16500}{2.303\times 8.314\times 298}$$
$$\therefore K_{p} = 779.41\ atm^{-1}$$
Also,
$$K_{p_{1}}$$ for $$N_{2} + 3H_{2}\rightleftharpoons 2NH_{3}$$
$$K_{p_{1}} = (K_{p})^{2} = (779.41)^{2}$$
$$K_{p_{1}} = 6.07\times 10^{5} atm^{-2}$$
Also,
$$-\triangle G^{\circ}_{1} = 2.303\times 8.314\times 298 \log (6.07\times 10^{5})J$$
$$= 32.998\ kJ$$
$$\therefore \triangle G^{\circ}_{1} = -32.998\ kJ\ mol^{-1}$$.