[adianadiadi]

I found the product ratio of para to ortho to meta ratio in the nitration of aniline to be 51% : 2% : 47%.

As per explanation given by textbooks...Even though in acidic medium aniline is converted to anilinium ion and the NH₃⁺ is strongly deactivating, the formation of para isomer is due to presence of free base in equilibrium with the cation. The para isomer is formed from the free base. This will shift the equilibrium, thus by improving the chances of formation of para isomer.

However, if para is formed from the free base, then why not ortho is also formed in appreciable quantity? It is only 2%. ...?

[pgk]

As you have already mentioned, there is an equilibrium between the free base and the cation.
On the other hand, the regioselective nitration of the free base, is driven by the formation of the conjugative o- and p- iminium-benzanion forms, respectively.
Question: Which iminium-benzanion form, is expected to shift the free base/cation equilibrium, more strongly; the para- or the ortho- conjugative form and why?

[adianadiadi]

As you have already mentioned, there is an equilibrium between the free base and the cation.
On the other hand, the regioselective nitration of the free base, is driven by the formation of the conjugative o- and p- iminium-benzanion forms, respectively.
Question: Which iminium-benzanion form, is expected to shift the free base/cation equilibrium, more strongly; the para- or the ortho- conjugative form and why?

Since charge separation is less in so called ortho iminium benzanion is less, it is expected to be more stable and shifts the equilibrium more rapidly...Then one must expect ortho to be formed in more quantity.

[pgk]

Please, do not mix electrostatic Physics with conjugation, which is something different.
Roughly, conjugation is a generation of a cloud of rolling electrons that commonly belongs to all participant atoms, which forms an intermediate structure with lower energy content. Often, the various conjugative forms do not equally contribute to conjugation. Furthermore, the density of the rolling electrons cloud is not equal to all atoms of a conjugative form, which creates positively and negatively charged atoms. Thus, the formation of a conjugative anion/cation pair is a dynamic phenomenon that follows the laws of Thermodynamics and not the Coulomb law of Electrostatics.
In other words, the para- iminium benzanion is more thermodynamically stable due to the more extended conjugation and will selectively shift the equilibrium.

[Ayushmaan]

The thing is that on ortho position NO2 group has a very strong-I effect on the NH3 group which will decrease the overall stability.

 so we won't get much of ortho nitro aniline

[pgk]

In conjugated-unsaturated systems, the strength of I+/I- effect is independent of its position; meaning α- or γ-, etc., due to the undisrupted flow of electrons through conjugation.

[adianadiadi]

Please, do not mix electrostatic Physics with conjugation, which is something different.
Thus, the formation of a conjugative anion/cation pair is a dynamic phenomenon that follows the laws of Thermodynamics and not the Coulomb law of Electrostatics.
In other words, the para- iminium benzanion is more thermodynamically stable due to the more extended conjugation and will selectively shift the equilibrium.

Sorry. I do not follow this point. What is the connection between laws of thermodynamics and stability of para with more extended conjugation? Could you please elaborate this? Do you think extended conjugation over many atoms will stabilize the system to more extent? Which law of thermodynamics explains this? Thank you.

[pgk]

Conjugation is created by the overlapping of neighboring π orbitals. Neighboring cations and anions, as well as free electron pairs may also participate in conjugation (resonance). Conjugation generates a cloud of rolling electrons that commonly belongs to all participant atoms, which forms an intermediate structure, as shown by X-ray diffraction analysis and recently, by atomic force microscopy. Sometimes, conjugation leads to additional or different chemical properties of the intermediate structure than expected (1,4-addition, aromaticity, etc.). Thus, conjugative forms (mesomers) are not isolable, in general.
There are many types conjugation, such as allylic conjugation, allylidene conjugation (e.g. butadiene conjugation), aromatic/heteroaromatic conjugation, hyperconjugation, etc. An exceptional case of conjugation is tautomerism because tautomers can chemically be separable and seen by IR and NMR spectrometry (e.g. ketone-enol tautomerism).
As a rule: “Conjugation stabilizes the molecule by decreasing the free energy (Gibbs equation) and therefore, the more extended conjugation (more participant atoms), the higher the stability is (compare: butadiene/benzene).”
The latter is proven by calorimetric analysis, which results lower enthalpies of hydrogenation or combustion than calculated by the Hess law. Besides, conjugation is also proven by UV spectrometry (bathochromy-auxochromy as interpreted by the Woodward-Fieser rules).
This is enough to know, in order to study reaction mechanisms and other issues of Organic Chemistry. Furthermore and if being more interested, the "why" and the "how much" conjugation decreases the free energy, are questions of Quantum Chemistry and their exact answers derive from quantum equations. 
 

[orgopete]

I found the product ratio of para to ortho to meta ratio in the nitration of aniline to be 51% : 2% : 47%.
...
However, if para is formed from the free base, then why not ortho is also formed in appreciable quantity? It is only 2%. ...?

Just so I understand this. Is this your data from your experiment? I think I often see ratios listed as ortho, meta, para. Since the order has been changed, is the data correct?

Aniline is very electrophilic and does not require as vigorous conditions to effect reaction. In order to get a high ratio of meta reaction, the conditions require strongly acidic conditions. With the high amount of para product, what were the nitration conditions?