$1\;g$ of impure $Na_2CO_3$ is dissolved in water and the solution is made upto $250\;ml$. To $50\;ml$ of this made up solution, $50\;ml$ of $0.1\;N\; HCl$ is added and the mixture after shaking well, required $10\;ml$ of $0.16\;N\; NaOH$ solution for complete neutralization. Calculate $\%$ purity of the sample of $Na_2CO_3$
