According to Henderson–Hasselbalch Equation,
pH = pKa + log [Nitrate] / [Nitric Acid]
As, Ka of Nitric Acid = 7.1 × 10⁻⁴
So,
pKa = -log [ 7.1 × 10⁻⁴ ]
pKa = 3.148
So, pH = 3.148 + log [Nitrate] / [Nitric Acid]
3.90 = 3.148 + log [Nitrate] / [Nitric Acid]
3.90 - 3.148 = log [Nitrate] / [Nitric Acid]
0.752 = log [Nitrate] / [Nitric Acid]
Taking Antilog on both sides,
[Nitrate] / [Nitric Acid] = 5.64