A sealed container was filled with $0\mathrm{.}3mol{H}_{2(g)},0\mathrm{.}4mol{I}_{2(g)},$ and $0\mathrm{.}2molH{I}_{(g)}$ at $870K$ and total pressure $1$ bar. Equilibrium constant $(K_{870}K)$ is $870$ for the reaction given below.

$H_{2(g)}+I_{2(g)}<mn\; id="EditorElement\_1381304">2</mn><mi\; id="EditorElement\_1381305">H</mi><msub\; id="EditorElement\_1381311"><mrow><mi\; id="EditorElement\_1381306">I</mi></mrow><mrow\; id="EditorElement\_1381310"><mi\; id="EditorElement\_1381307">(</mi><mi\; id="EditorElement\_1381308">g</mi><mi\; id="EditorElement\_1381309">)</mi></mrow></msub>$

a$)$ Calculate the reaction coordinate and amounts of the components in the mixture at equilibrium.

b$)$ Calculate the change in the equilibrium constant of the reaction when the total pressure is increased from $1$ bar to $2$ bar at constant temperature.