A tenfold increase in the pressure on the reaction,

${\mathrm{N}}_2\left(\mathrm{g}\right)+3{\mathrm{H}}_2\left(\mathrm{g}\right)\rightleftharpoons 2{\mathrm{NH}}_3\left(\mathrm{g}\right)$

at equilibrium, results in $\dots \dots$ ${\mathrm{K}}_{\mathrm{p}}$.

The reaction:

${\mathrm{Sb}}_2{\mathrm{S}}_3\left(\mathrm{s}\right)+3{\mathrm{H}}_2\left(\mathrm{g}\right)\rightleftharpoons 2\mathrm{Sb}\left(\mathrm{s}\right)+3{\mathrm{H}}_2\mathrm{S}\left(\mathrm{g}\right)$

was studied by analysing the equilibrium mixture for the amount of ${\mathrm{H}}_2\mathrm{S}$ produced. A vessel whose volume was $\text{2.5 litre}$ was filled with $0.01$mole of ${\mathrm{Sb}}_2{\mathrm{S}}_3$ and$0.01$ mole of ${\mathrm{H}}_2$. After the mixture came to equilibrium in the closed vessel at $440°\mathrm{C},$ the gaseous mixture was removed, and the ${\mathrm{H}}_2\mathrm{S}$ was dissolved in water. Sufficient ${\mathrm{Pb}}^{2+}$ ions were added to react completely with the ${\mathrm{H}}_2\mathrm{S}$ to precipitate $\mathrm{PbS}$ . If $1.029 \mathrm{g}$ of $\mathrm{PbS}$ was obtained, what is the value of ${\mathrm{K}}_{\mathrm{c}}$ at $440°\mathrm{C}?$

Give answer after multiplying with 100 and rounding off to the nearest integer value.

Although $\mathrm{AgCl}$ is insoluble in water, it readily dissolves upon the addition of ammonia $AgCl \left(\mathrm{s}\right)+2{\mathrm{NH}}_3 \left(\mathrm{aq}\right)\rightleftharpoons \mathrm{Ag}{\left({\mathrm{NH}}_3\right)}_2^{+} \left(\mathrm{aq}\right)+{\mathrm{Cl}}^{-} \left(\mathrm{aq}\right)$

What is the equilibrium constant for this dissolving process? (Report your answer after multiplying by 1000)

${\mathrm{K}}_{\mathrm{sp}}\left(\mathrm{AgCl}\right)=1.8\times {10}^{-10} \text{and }{\mathrm{K}}_{\mathrm{f}}\left[\mathrm{Ag}{\left({\mathrm{NH}}_3\right)}_2^{+}\right]=1.7\times {10}^7$

Although $\mathrm{AgCl}$ is insoluble in water, it readily dissolves upon the addition of ammonia. $AgCl\left(\mathrm{s}\right)+2{\mathrm{NH}}_3\left(\mathrm{aq}\right)\rightleftharpoons \mathrm{Ag}{\left({\mathrm{NH}}_3\right)}_2^{+}\left(\mathrm{aq}\right)+{\mathrm{Cl}}^{-}\left(\mathrm{aq}\right)$

Ammonia is added to a solution containing an excess of $\mathrm{AgCl}$ (s). The final volume is $1\mathrm{l}$, and the resulting equilibrium concentration of ${\mathrm{NH}}_3$ is $0.80 \mathrm{M}$. Calculate the number of moles of $\mathrm{AgCl}$ dissolved, the molar concentration of $Ag{\left({\mathrm{NH}}_3\right)}_2^{+}$ , and the number of moles of ${\mathrm{NH}}_3$ added to the original solution.

${\mathrm{K}}_{\mathrm{sp}}\left(\mathrm{AgCl}\right)=1.8\times {10}^{-10} \text{and }{\mathrm{K}}_{\mathrm{f}}\left[\mathrm{Ag}{\left({\mathrm{NH}}_3\right)}_2^{+}\right]=1.7\times {10}^7$

From the dissociation constants, ${\mathrm{K}}_{\mathrm{a}}$ and ${\mathrm{K}}_{\mathrm{b}}$ for an acid and its conjugate base, show that ${\mathrm{K}}_{\mathrm{a}}·{\mathrm{K}}_{\mathrm{b}}={\mathrm{K}}_{\mathrm{w}}$.

The tallest trees known are the redwoods in California. Assuming the height of a redwood tree to be $105 \mathrm{m}$, estimate the osmotic pressure required to push water up from the roots to the treetop. $\left({\mathrm{d}}_{{\mathrm{H}}_2\mathrm{O}}=1 \mathrm{g}/\mathrm{cc}, \mathrm{g}=9.8 \mathrm{m} {\mathrm{s}}^{-2}\right)$

If the answer is of type $\mathrm{y}\times {10}^6 \mathrm{Pa}$, mention the value of $\mathrm{y}$ correct up to nearest integer value.

A sample of impure cuprite, ${\mathrm{Cu}}_2\mathrm{O}$, contains $66.6\%$ copper. Calculate the percentage of pure ${\mathrm{Cu}}_2\mathrm{O}$ in the sample. $\left(\mathrm{Cu}=63.5, \mathrm{O}=16\right)$

Round-off your answer to the nearest integer.

How much of ${\mathrm{Ag}}^{+}$would remain in the solution after mixing equal volumes of $0.08 \mathrm{M}$ ${\mathrm{AgNO}}_3$ and $0.08 \mathrm{M} \mathrm{HOCN}$ ? ${\mathrm{K}}_{\mathrm{a} }\left(\mathrm{HOCN}\right)=3.3\times {10}^{-4} {\mathrm{K}}_{\mathrm{sp} }\left(\mathrm{AgOCN}\right)=2.3\times {10}^{-7}$

If the answer is of type $\mathrm{y}\times {10}^{-4} \mathrm{M}$, report the value of $\mathrm{y}$ correct up to nearest integer value.