Tin is obtained from cassiterite by reduction with coke. Use the data given below to determine the minimum temperature (in K ) at which the reduction of cassiterite by coke would take place.

\(298 K: \Delta_{ f } H ^0\left( SnO _2(s)\right)=-581.0 kJ mol ^{-1}\), \(\Delta_{ f } H ^0\left( CO _2(g)\right)=-394.0 kJ mol ^{-1}\)

\(S ^0\left( SnO _2(s)\right)=56.0 JK ^{-1} mol^{-1}, S^0( Sn ( s ))\) \(=52.0 JK ^{-1} mol^{-1}\)

\(S ^0( C ( s ))=6.0 JK ^{-1} mol^{-1}, S^0\left( CO _2(g)\right)\) \(=210.0 JK ^{-1} mol^{-1}\)

Assume that the enthalpies and the entropies are temperature independent.

Consider a reaction \(A+R \rightarrow\) Product. The rate of this reaction is measured to be \(k[A][R]\). At the start of the reaction, the concentration of \(R,[R]_0\), is 10 -times the concentration of \(A,[A]_0\). The reaction can be considered to be a pseudo first order reaction with assumption that \(k[R]=k^{\prime}\) is constant. Due to this assumption, the relative error (in \%) in the rate when this reaction is \(40 \%\) complete, is _______
[ \(k\) and \(k^{\prime}\) represent corresponding rate constants]

The conductance of $0.0015\mathrm{ }\mathrm{M}$ aqueous solution of a weak monobasic acid was determined by using a conductivity cell consisting of platinized $\mathrm{Pt}$electrodes. The distance between the electrodes is $120\mathrm{ }\mathrm{cm}$ with an area of cross-section of $1 {\mathrm{cm}}^2$. The conductance of this solution was found to be $5\times {10}^{-7}\mathrm{S}$ . The $\mathrm{pH}$of the solution is $4$. The value of limiting molar conductivity of this weak monobasic acid in aqueous solution is $\mathrm{ }\mathrm{Z}\mathrm{ }\times \mathrm{ }{10}^2\mathrm{S}\mathrm{ }{\mathrm{cm}}^{-1}{\mathrm{mol}}^{-1}.$ The value of $\mathrm{Z}$is.

For one mole of a van der Waal's gas when \(b=0\) and \(\mathrm{T}=300 \mathrm{~K}\), the PV vs, \(1 / \mathrm{V}\) plot is shown below. The value of the van der Waal's constant \(a\) (atm. liter \({ }^{2} \mathrm{~mol}^{-2}\) ) is :

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The coordination number of \(\mathrm{Ni}^{2+}\) is 4 .
\(\mathrm{NiCl}_2+\mathrm{KCN}\) (excess) \(\rightarrow A\) (cyano complex)
\(\mathrm{NiCl}_2+\) conc. \(\mathrm{HCl}\) (excess) \(\rightarrow B\) (chloro complex)
Question:
Predict the magnetic nature of \(A\) and \(B\) are

In the following reaction sequence, the major product \(\mathbf{P}\) is formed.

Glycerol reacts completely with excess \(\mathbf{P}\) in the presence of an acid catalyst to form \(\mathbf{Q}\). Reaction of \(\mathbf{Q}\) with excess \(\mathrm{NaOH}\) followed by the treatment with \(\mathrm{CaCl}_2\) yields Ca-soap \(\mathbf{R}\), quantitatively. Starting with one mole of \(\mathbf{Q}\), the amount of \(\mathbf{R}\) produced in gram is ________.
[Given, atomic weight: \(\mathrm{H}=1, \mathrm{C}=12,\) \(\mathrm{~N}=14, \mathrm{O}=16, \mathrm{Na}=23, \mathrm{Cl}=35,\) \(\mathrm{Ca}=40\)]

The reaction of $\mathrm{Pb}{\left({\mathrm{NO}}_3\right)}_2$ and $\mathrm{NaCl}$ in water produces a precipitate that dissolves upon the addition of $\mathrm{HCl}$ of appropriate concentration. The dissolution of the precipitate is due to the formation of

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Tollen's reagent is used for the detection of aldehyde when a solution of \(\mathrm{AgNO}_3\) is added to glucose with \(\mathrm{NH}_4 \mathrm{OH}\) then gluconic acid is formed
\(\mathrm{Ag}^{+}+e^{-} \rightarrow \mathrm{Ag} E_{\text {red }}^{\circ}=0.8 \mathrm{~V} \)
\( \mathrm{C}_6 \mathrm{H}_{12} \mathrm{O}_6+\mathrm{H}_2 \mathrm{O} \rightarrow \text { Gluconic acid }\left(\mathrm{C}_6 \mathrm{H}_{12} \mathrm{O}_7\right)\) \(+~2 \mathrm{H}^{+}+2 e^{-} ; -E_{\mathrm{red}}^{\circ}=-0.05 \mathrm{~V} \)
\( \mathrm{Ag}\left(\mathrm{NH}_3\right)_2^{+}+e^{-} \rightarrow \mathrm{Ag}(s)+2 \mathrm{NH}_3 ;\) \(E_{\mathrm{red}}^{\circ}=0.337 \mathrm{~V}\)
[Use \(2.303 \times \frac{R T}{F}=0.0592\) and \(\frac{F}{R T}=38.92\) at \(298 \mathrm{~K}\) ]
Question:
When ammonia is added to the solution, \(\mathrm{pH}\) is raised to 11 . Which half-cell reaction is affected by \(\mathrm{pH}\) and by how much?

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A fixed mass $\text{'}\mathrm{m}\text{'}$ of a gas is subjected to transformation of states from $\mathrm{K}$ to $\mathrm{L}$ to $\mathrm{M}$ to $\mathrm{N}$ and back to $\mathrm{K}$ as shown in the figure

Question :
The succeeding operations that enable this transformation of states are

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A wooden cylinder of diameter \(4 r\), height \(H\) and density \(\rho / 3\) is kept on a hole of diameter \(2 r\) of a tank, filled with liquid of density \(\rho\) as shown in the figure.

Question :
The block in the above question is maintained at the position by external means and the level of liquid is lowered. The height \(h_2\) when this external force reduces to zero is

Two uniform strings of mass per unit length \(\mu\) and \(4 \mu\), and length \(L\) and \(2 L\), respectively, are joined at point \(\mathrm{O}\), and tied at two fixed ends \(\mathrm{P}\) and \(\mathrm{Q}\), as shown in the figure. The strings are under a uniform tension \(T\). If we define the frequency \(v_0=\frac{1}{2 L} \sqrt{\frac{T}{\mu}}\), which of the following statement(s) is(are) correct?

Three numbers are chosen at random, one after another with replacement, from the set \(S=\{1,2,3, \ldots, 100\}\). Let \(p_{1}\) be the probability that the maximum of chosen numbers is at least 81 and \(p_{2}\) be the probability that the minimum of chosen numbers is at most 40 .
The value of $\frac{625}{4}{p}_1$ is

A crystalline solid of a pure substance has a face-centred cubic structure with a cell edge of $400\mathrm{ }\mathrm{pm}$ . If the density of the substance in the crystal is $8 \mathrm{g}\mathrm{ }{\mathrm{cm}}^{-3},\mathrm{ }$ then the number of atoms present in $256 \mathrm{g}$ of the crystal $\mathrm{is}\mathrm{ }\mathrm{N}\mathrm{ }\times \mathrm{ }{10}^{24}$ . The value of $\mathrm{N}$is