For the equation ${\mathrm{CaCO}}_3 \left(\mathrm{s}\right)\to \mathrm{CaO} \left(\mathrm{s}\right)+{\mathrm{CO}}_2 \left(\mathrm{g}\right), {\mathrm{K}}_{1000}=0.059.$ Exactly $10 \mathrm{g}$ of ${\mathrm{CaCO}}_3$ is placed in a $10 \mathrm{L}$ container at $1000 \mathrm{K}$. After equilibrium is reached, what mass of ${\mathrm{CaCO}}_3$ remains?

Round off the answer to the nearest integer.

A mixture of nitrogen and hydrogen in a proportion of $1 : 3$ by volume was subjected to a pressure of $30 \mathrm{atm}$ and a temperature of $723 \mathrm{K}$. After equilibrium was established, the analysis indicated that the mixture contained $6\%$ of ammonia by volume, Calculate ${\mathrm{K}}_{\mathrm{p}}$.

[Express ${\mathrm{K}}_{\mathrm{P}}$ in terms of ${10}^{-5}$ ${\mathrm{atm}}^{-2}$]

For the reaction ${\left[\mathrm{Ag}(\mathrm{CN}{)}_2\right]}^{-}\rightleftharpoons {\mathrm{Ag}}^{+}+2{\mathrm{CN}}^{-},$ the equilibrium constant at $25°\mathrm{C}$ is $4\times {10}^{-19}$. Calculate the silver ion concentration in a solution which was originally $0.1$molar in $\mathrm{KCN}$ and $0.03$ molar in ${\mathrm{AgNO}}_3$. If your answer is $\mathrm{y} \times {10}^{-18 }, \mathrm{then} \mathrm{y} \mathrm{is}$:

$2.5 \mathrm{mL}$ of $\frac{2}{5} \mathrm{M}$ weak monoacidic base $\left({\mathrm{K}}_{\mathrm{b}}=1\times {10}^{-12} \text{at} 25°\mathrm{C}\right)$ is titrated with $\frac{2}{15} \mathrm{M} \mathrm{HCl}$ in water at $25°\mathrm{C}$. The concentration of ${\mathrm{H}}^{+}$ at the equivalence point is $\left({\mathrm{K}}_{\mathrm{w}}=1\times {10}^{-14} \text{at} 25°\mathrm{C}\right)$.

(Hint: The base is very weak, the cations of the salt formed at the equivalence point shall undergo hydrolysis to a greater extent and, hence, the degree of hydrolysis $\left(\mathrm{h}\right)$ cannot be neglected in comparison to $1$. Now, apply ${\mathrm{K}}_{\mathrm{h}}=\frac{{\mathrm{Ch}}^2}{1-\mathrm{h}}=\frac{{\mathrm{K}}_{\mathrm{w}}}{{\mathrm{K}}_{\mathrm{b}}}; \mathrm{C}=0.1 \mathrm{M}, \left[{\mathrm{H}}^{+}\right]=\mathrm{Ch}$).

Assertion: The addition of an inert gas at a constant volume may affect the state of the equilibrium: ${\mathrm{PCl}}_5\left(\mathrm{g}\right)\rightleftharpoons {\mathrm{PCl}}_3\left(\mathrm{g}\right)+{\mathrm{Cl}}_2\left(\mathrm{g}\right)$

Reason: The addition of an inert gas at a constant volume increases both the number of molecules and the pressure to the same extent.