If both the functional groups of salicylic acid, ${\mathrm{HOC}}_6{\mathrm{H}}_4\mathrm{COOH}$, ionise in water with ${\mathrm{K}}_{\mathrm{a}}=1\times {10}^{-3}$ for the $-\mathrm{COOH}$ group and $4.2\times {10}^{-13}$ for the $-\mathrm{OH}$ group, calculate $\mathrm{pH}$ of the saturated solution of the acid (solubility $=1.8 \mathrm{g}/\mathrm{L}$).

The density of trifluoroacetic acid vapour was determined at $117 °\mathrm{C}$ and $470 \mathrm{mm} \mathrm{Hg}$ and was found to be $2.784 \mathrm{g}/\mathrm{L}$. Calculate ${\mathrm{K}}_{\mathrm{c}}$ for:

The following equilibrium exist simultaneously in a vessel.

$2{\mathrm{NO}}_2\left(\mathrm{g}\right)\rightleftharpoons {\mathrm{N}}_2{\mathrm{O}}_4\left(\mathrm{g}\right); {\mathrm{K}}_{{\mathrm{p}}_1}=6.8 {\mathrm{atm}}^{-1}$

$\mathrm{NO}\left(\mathrm{g}\right)+{\mathrm{NO}}_2\left(\mathrm{g}\right)\rightleftharpoons {\mathrm{N}}_2{\mathrm{O}}_3\left(\mathrm{g}\right); {\mathrm{K}}_{{\mathrm{p}}_2}\left(\text{ say }\right)$

If initially only $\mathrm{NO}$ and ${\mathrm{NO}}_2$ are present in $1 : 2 \mathrm{mole}$ ratio and the total pressure at equilibrium is $5.05 \mathrm{atm}$ and the partial pressure of ${\mathrm{N}}_2{\mathrm{O}}_4$ is $1.7 \mathrm{atm},$ calculate the equilibrium partial pressure of $\mathrm{NO}$ and ${\mathrm{K}}_{{\mathrm{p}}_2}$.

In a reaction of the type:

$\mathrm{A}\left(\mathrm{s}\right)+2\mathrm{B}\left(\mathrm{g}\right)\rightleftharpoons \mathrm{C}\left(\mathrm{g}\right)+\mathrm{D}\left(\mathrm{g}\right)$

the equilibrium concentrations of $\mathrm{A}, \mathrm{B}, \mathrm{C}$ and $\mathrm{D}$ are $1, 2, 5$and $6 \frac{\mathrm{mol}}{\mathrm{litre}}$ respectively. Argon is then introduced at equilibrium at constant volume. Calculate the concentrations of $\mathrm{A}, \mathrm{B}, \mathrm{C}$ and $\mathrm{D}$ at the new equilibrium positions.

The rate law of the reaction given below is given as $2 \mathrm{A}+\mathrm{B}\to$ product.

Rate$=\mathrm{k}{\left[\mathrm{A}\right]}^2\left[\mathrm{B}\right]$

Find $\mathrm{x}$.

Nitric acid is prepared from ammonia in a three-step process:

(i) $4{\mathrm{NH}}_3+5{\mathrm{O}}_2\to 4\mathrm{NO}+6{\mathrm{H}}_2\mathrm{O}$ (fast)

(ii) $2\mathrm{NO}+{\mathrm{O}}_2\to 2{\mathrm{NO}}_2$ (slow)

(iii) $3{\mathrm{NO}}_2+{\mathrm{H}}_2\mathrm{O}\to 2{\mathrm{HNO}}_3+\mathrm{NO}$ (fast)

Calculate how much ${\mathrm{HNO}}_3$ can be produced from ${10}^5 \mathrm{kg}$ of ammonia assuming $100\%$ efficiency in each of the reactions.

If the answer is of type $\mathrm{y}\times {10}^5 \mathrm{kg}$, report the value of $\mathrm{y}$ correct up to two places of decimals.

If given chemical reaction is a second-order in $\mathrm{NO}$ and first-order in ${\mathrm{O}}_2$, calculate the rate of formation of ${\mathrm{HNO}}_3$ when oxygen concentration is $0.50 \mathrm{M}$ and the nitric oxide concentration is $0.75 \mathrm{M}.$

$4\mathrm{NO}+3{\mathrm{O}}_2+2{\mathrm{H}}_2\mathrm{O}\stackrel{}{ \to }4{\mathrm{HNO}}_3 ; \mathrm{k}=5.8\times {10}^2 {\mathrm{L}}^6 {\mathrm{mol}}^{-2} {\mathrm{s}}^{-1}$

When an electron in an excited molybdenum atom falls from $\mathrm{L} \mathrm{to} \mathrm{K}$ shell, an X -ray is emitted. These X-rays are diffracted at an angle of $7.75°$ by planes with a separation of $2.64 \stackrel{\mathrm{o}}{\mathrm{A}}$. What is the difference in energy in joules between the $\mathrm{K}$ shell and the $\mathrm{L}$ shell in $\mathrm{Mo}$ assuming a first-order diffraction?

If the answer is of type $\mathrm{y}\times {10}^{-15} \mathrm{J}$, report the value of $\mathrm{y}$ correct up to two places of decimals.