A definite amount of solid $N{H}_{4}HS$ is placed in a flask already containing ammonia gas at a certain temperature and 0.1 atm pressure. $N{H}_{4}HS$ decompses to give $N{H}_3$ and $H_{2}S$ and at equilibrium total pressure in flask is 1.1 atm. If the equilibrium constant $K_P$ for the reaction $N{H}_{4}HS\left(s\right)\iff N{H}_3\left(g\right)+H_{2}S\left(g\right)$ is represented as $z\times {10}^{-1}$ then find the value of z.

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