Physical Chemistry PYQ — Page 7

Consider the following aqueous solutions. I. 2.2 g Glucose in 125 mL of solution. II. 1.9 g Calcium chloride in 250 mL of solution. III. 9.0 g Urea in 500 mL of solution. IV. 20.5 g Aluminium sulphate in 750 mL of solution. The correct increasing order of boiling point of these solutions will be : [Given : Molar mass in $\mathrm{g} \mathrm{mol}^{-1}: \mathrm{H}=1, \mathrm{C}=12, \mathrm{~N}=14, \mathrm{O}=16, \mathrm{Cl}=35.5, \mathrm{Ca}=40, \mathrm{Al}=27$ and $\mathrm{S}=32$]

Consider the first order reaction $R \rightarrow P$. The fraction of molecules decomposed in the given first order reaction can be expressed as

Consider the dissociation equilibrium of the following weak acid $\mathrm{HA} \rightleftharpoons \mathrm{H}^{+}(\mathrm{aq})+\mathrm{A}^{-}(\mathrm{aq})$ If the pKa of the acid is 4, then the pH of 10 mMHA solution is $\_\_\_\_$.(Nearest integer) [Given: The degree of dissociation can be neglected with respect to unity]

Consider $\mathrm{A} \xrightarrow{\mathrm{k}_{1}} \mathrm{~B}$ and $\mathrm{C} \xrightarrow{\mathrm{k}_{2}} \mathrm{D}$ are two reactions. If the rate constant $\left(\mathrm{k}_{1}\right)$ of the $\mathrm{A} \longrightarrow \mathrm{B}$ reaction can be expressed by the following equation $\log _{10} \mathrm{k}=14.34-\frac{1.5 \times 10^{4}}{\mathrm{~T} / \mathrm{K}}$ and activation energy of $C \longrightarrow D$ reaction $\left(E a_{2}\right)$ is $\frac{1}{5}$ th of the $A \longrightarrow B$ reaction $\left(E a_{1}\right)$, then the value of $\left(E a_{2}\right)$ is $\_\_\_\_$ $\mathrm{kJ} \mathrm{mol}^{-1}$. (Nearest Integer)

Consider a weak base ' B ' of $\mathrm{pK}_{\mathrm{b}}=5.699$. ' $x$ ' mL of 0.02 M HCl and ' y ' mL of 0.02 M weak base ' B ' are mixed to make 100 mL of a buffer of pH 9 at $25^{\circ} \mathrm{C}$. The values of ' $x$ ' and ' $y$ ' respectively are: [Given: $\log 2=0.3010, \log 3=0.4771, \log 5=0.699$]

Consider a solution of $\mathrm{CO}_{2}(\mathrm{~g})$ dissolved in water in a closed container. Which one of the following plots correctly represents variation of log (partial pressure of $\mathrm{CO}_{2}$ in vapour phase above water) $[y$-axis] with $\log$ (mole fraction of $\mathrm{CO}_{2}$ in water) $[x$-axis $]$ at $25^{\circ} \mathrm{C}$ ?

At the transition temperature $T$, $A \rightleftharpoons B$ and $\Delta G^0 = 105 - 35\log T$ where $A$ and $B$ are two states of substance $X$. The transition temperature in $°$C when pressure is $1$ atm is _______. (Nearest integer)

At $298\text{ K}$, the molar conductivity of $x\%$ (w/w) $MX$ solution (aqueous) is $123.5\text{ S cm}^2\text{ mol}^{-1}$. The conductance of same solution is $1.9 \times 10^{-3}\text{ S}$. The value of $x$ is _______ $\times 10^{-2}$. (Given : cell constant $= 1.3\text{ cm}^{-1}$; molar mass of $MX$ is $75\text{ g mol}^{-1}$, density of aqueous solution of $MX$ at $298\text{ K}$ is $1.0\text{ g mL}^{-1}$)

At $T(K)$, the equilibrium constant of $A_2(g) + B_2(g) \rightleftharpoons C(g)$ is $2.7 \times 10^{-5}$. What is the equilibrium constant for $\dfrac{1}{3}A_2(g) + \dfrac{1}{3}B_2(g) \rightleftharpoons \dfrac{1}{3}C(g)$ at the same temperature?

At $\mathrm{T}(\mathrm{K}), 100 \mathrm{~g}$ of $98 \% \mathrm{H}_{2} \mathrm{SO}_{4}(\mathrm{w} / \mathrm{w})$ aqueous solution is mixed with 100 g of $49 \% \mathrm{H}_{2} \mathrm{SO}_{4}(\mathrm{w} / \mathrm{w})$ aqueous solution. What is the mole fraction of $\mathrm{H}_{2} \mathrm{SO}_{4}$ in the resultant solution? (Given : Atomic mass $\mathrm{H}=1 \mathrm{u} ; \mathrm{S}=32 \mathrm{u} ; \mathrm{O}=16 \mathrm{u}$). (Assume that temperature after mixing remains constant)

At $\mathrm{T}(\mathrm{K}), 2$ moles of liquid A and 3 moles of liquid B are mixed. The vapour pressure of ideal solution formed is 320 mm Hg. At this stage, one mole of A and one mole of B are added to the solution. The vapour pressure is now measured as 328.6 mm Hg. The vapour pressure (in mm Hg) of A and B are respectively:

At $25°C$, $20.0$ mL of $0.2$ M weak monoprotic acid HX is titrated against $0.2$ M NaOH. The pH of the solution (a) at the start of the titration (when NaOH has not been added) and (b) when $10$ mL of NaOH is added respectively, are: Given: $K_a = 5 \times 10^{-4}$, $pK_a = 3.3$, $\alpha << 1$ <table class="pyq-table"><tbody><tr><th>(a)</th><th>(b)</th></tr></tbody></table>

At $27^{\circ} \mathrm{C}$ in presence of a catalyst, activation energy of a reaction is lowered by $10 \mathrm{~kJ} \mathrm{~mol}^{-1}$. The logarithm of ratio of $\frac{\mathrm{k} \text { (catalysed) }}{\mathrm{k} \text { (uncatalysed) }}$ is.... (Consider that the frequency factor for both the reactions is same)

At $27°$C, $0.1$ M, $1$ L $K_4[Fe(CN)_6]$ aqueous solution and $0.1$ M, $1$ L $FeCl_3$ aqueous solution are placed in a container separated by a semi permeable membrane AB. Assume complete dissociation of both the solutes. Which of the following statement is correct? 

At 298 K, the mole percentage of $\mathrm{N}_{2}(\mathrm{~g})$ in air is $80 \%$. Water is in equilibrium with air at a pressure of 10 atm. What is the mole fraction of $\mathrm{N}_{2}(\mathrm{~g})$ in water at 298 K ? ($\mathrm{K}_{\mathrm{H}}$ for $\mathrm{N}_{2}$ is $6.5 \times 10^{7} \mathrm{~mm} \mathrm{Hg}$)

Arrange the following resultant mixtures in increasing order of their pH values A. $10$ mL $0.2$ M Ca(OH)$_2$ + $25$ mL $0.1$ M HCl B. $10$ mL $0.01$ M H$_2$SO$_4$ + $10$ mL $0.01$ M Ca(OH)$_2$ C. $10$ mL $0.1$ M H$_2$SO$_4$ + $10$ mL $0.1$ M KOH Choose the correct answer from the options given below:

Arrange the following isothermal processes in order of the magnitude of the work ($p - V$) involved between states $1$ and $2$. A. Expansion in single stage $w_A$ B. Expansion in multi stages $w_B$ C. Compression in single stage $w_C$ D. Compression in multi stages $w_D$ Choose the correct option.

Arrange the following atomic orbitals of multi electron atoms in order of increasing energy. A. $n = 3, l = 2, m = +1$ B. $n = 4, l = 0, m = 0$ C. $n = 6, l = 1, m = 0$ D. $n = 5, l = 1, m = +1$ E. $n = 2, l = 1, m = +1$ Choose the correct answer from the options given below:

Aqueous HCl reacts with $\mathrm{MnO}_{2}(\mathrm{~s})$ to form $\mathrm{MnCl}_{2}(\mathrm{aq}), \mathrm{Cl}_{2}(\mathrm{~g})$ and $\mathrm{H}_{2} \mathrm{O}(l)$. What is the weight (in g) of $\mathrm{Cl}_{2}$ liberated when 8.7 g of $\mathrm{MnO}_{2}(\mathrm{~s})$ is reacted with excess aqueous HCl solution? (Given Molar mass in $\mathrm{g} \mathrm{mol}^{-1} \mathrm{Mn}=55, \mathrm{Cl}=35.5, \mathrm{O}=16, \mathrm{H}=1$)

$\mathrm{X}_{2}(\mathrm{~g})+\mathrm{Y}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{Z}(\mathrm{g})$ $\mathrm{X}_{2}(\mathrm{~g})$ and $\mathrm{Y}_{2}(\mathrm{~g})$ are added to a 1 L flask and it is found that the system attains the above equilibrium at $\mathrm{T}(\mathrm{K})$ with the number of moles of $\mathrm{X}_{2}(\mathrm{~g}), \mathrm{Y}_{2}(\mathrm{~g})$ and $\mathrm{Z}(\mathrm{g})$ being 3,3 and 9 mol respectively (equilibrium moles). Under this condition of equilibrium, 10 mol of $\mathrm{Z}(\mathrm{g})$ is added to the flask and the temperature is maintained at $\mathrm{T}(\mathrm{K})$. Then the number of moles of $\mathrm{Z}(\mathrm{g})$ in the flask when the new equilibrium is established is $\_\_\_\_$. (Nearest integer)

An oxide of iron contains $69.9\%$ iron, its empirical formula, is: (Given: Molar mass of Fe and O are $56$ and $16$ g mol$^{-1}$ respectively.)

An oxide of iron contains $69.9\%$ iron, its empirical formula, is: (Given: Molar mass of Fe and O are $56$ and $16$ g mol$^{-1}$ respectively.)

An organic compound undergoes first order decomposition. The time taken for decomposition to $\left(\frac{1}{8}\right)^{\text {th }}$ and $\left(\frac{1}{10}\right)^{\text {th }}$ of its initial concentration are $\mathrm{t}_{1 / 8}$ and $\mathrm{t}_{1 / 10}$ respectively. What is the value of $\frac{\mathrm{t}_{1 / 8}}{\mathrm{t}_{1 / 10}} \times 10$ ? ($\log 2=0.3$)

An electrochemical cell is constructed using half cells in the direction of spontaneous change $Fe(OH)_2(s) + 2e^- \rightarrow Fe(s) + 2OH^-(aq) \quad E^\theta = -0.88$ V and $AgBr(s) + e^- \rightarrow Ag(s) + Br^-(aq) \quad E^\theta = +0.07$ V Which of the following option is correct?