Question

On the basis of le chatelier's principle explain why ag2co3 dissolves when hno3 is added

Answer 1

The reaction is an equilibrium represented by the equation 

Ag2CO3(s) + 2 HNO3(aq) <----> 2 AgNO3(aq) + H2O(l) + CO2(g) 

From the Le Chatelier's Principle which states that changing a factor such as concentration, temperature, or pressure of a reaction at equilibrium will cause the reaction to shift in the direction that counteracts the effect of that change. 
Therefore; the CO2 produced starts escaping and the concentration and pressure of CO2 drops. The system responds by trying to increase the concentration and pressure of CO2 by producing more. This means more and more Ag2CO3 will dissolve due to reaction with the acid, HNO3. 
This continues until one of the reactants is exhausted. 

Answer 2

Silver carbonate dissociates and show equilibrium as shown below

$AgNO_{3}(s)--->Ag^{+}(aq)+CO_{3}^{-2}$

so there is formation of carbonate ions

When we add strong acid nitric acid in it , it gives proton (hydronium ion)

These $H^{+}$ reacts with carbonate ions and thus decreases the concentration of carbonate ions in the solution. Due to decrease in concentration products the system will shift in the direction where there can be an increase in concentration of products. Hence system or equilibrium shifts in forward direction. This will cause more solubility of silver carbonate Or we can say that the silver carbonate dissolves