JEE MainsJEE AdvanceBITSAT

JEE Mains | PYQ

The pressure exerted by a non-reactive gaseous mixture of \( 6.4 \, \text{g} \) of methane and \( 8.8 \, \text{g} \) of carbon dioxide in a \( 10 \, \text{L} \) vessel at \( 27^\circ \text{C} \) is ______ \( \text{kPa} \).
(Round off to the Nearest Integer).
[Assume gases are ideal, \( R = 8.314 \, \text{J mol}^{-1}\text{K}^{-1} \)
Atomic mass : \( \mathrm{C:12.0 \, u, \ H:1.0 \, u, \ O:16.0 \, u} \)]

The incorrect expression among the following is:

For water at \( 100^\circ \text{C} \) and \( 1 \) \( \text{bar} \), \( \Delta_{\text{vap}}H - \Delta_{\text{vap}}U = \) ______ \( \times 10^{2} \) \( \text{J mol}^{-1} \). (Round off to the Nearest Integer)
[Use : \( R = 8.31 \) \( \text{J mol}^{-1} \text{K}^{-1} \)]
[Assume volume of \( \mathrm{H_2O{(l)}} \) is much smaller than volume of \( \mathrm{H_2O{(g)}} \). Assume \( \mathrm{H_2O{(g)}} \) can be treated as an ideal gas]

The gas phase reaction \( 2A (g) \rightleftharpoons A_{2} (g) \) at \( 400 \, \mathrm{K} \) has \( \Delta G^{\circ} = +25.2 \, \mathrm{kJ \, mol^{-1}} \). The equilibrium constant \( K_c \) for this reaction is _____ \( \times 10^{-2} \).
[Use: \( R = 8.3 \, \mathrm{J \, mol^{-1} \, K^{-1}} \), \( \ln 10 = 2.3 \), \( \log_{10} 2 = 0.30 \), \( 1 \, \mathrm{atm} = 1 \, \mathrm{bar} \)]
[antilog \( (-0.3) = 0.501 \)]

A system does \( 200 \, \mathrm{J} \) of work and at the same time absorbs \( 150 \, \mathrm{J} \) of heat. The magnitude of the change in internal energy is _______ \( \mathrm{J} \). (Nearest integer)

An average person needs about \( 10000 \, \text{kJ} \) energy per day. The amount of glucose (molar mass \( = 180.0 \, \text{g mol}^{-1} \)) needed to meet this energy requirement is __________ \( \text{g} \). (Nearest integer)
(Use : \( \Delta_c H (\text{glucose}) = -2700 \, \text{kJ mol}^{-1} \).)

At \( 25^\circ \text{C} \), \( 50 \, \text{g} \) of iron reacts with HCl to form \( \mathrm{FeCl}_2 \). The evolved hydrogen gas expands against a constant pressure of \( 1 \, \text{bar} \). The work done by the gas during this expansion is __________ \( \text{J} \).
(Round off to the Nearest Integer). [Given : \( R = 8.314 \, \text{J mol}^{-1} \text{K}^{-1} \). Assume hydrogen is an ideal gas] [Atomic mass of Fe is \( 55.85 \, \text{u} \)]

For the reaction \( 2\text{NO}_2 (g) \rightleftharpoons \text{N}_2\text{O}_4 (g) \), when \( \Delta S = -176.0 \, \text{J K}^{-1} \) and \( \Delta H = -57.8 \, \text{kJ mol}^{-1} \), the magnitude of \( \Delta G \) at \( 298 \, \text{K} \) for the reaction is ____ \( \text{kJ mol}^{-1} \).

For a given chemical reaction \( A \rightarrow B \) at \( 300 \, \text{K} \) the free energy change is \( -49.4 \, \text{kJ mol}^{-1} \) and the enthalpy of reaction is \( 51.4 \, \text{kJ mol}^{-1} \). The entropy change of the reaction is __________ \( \text{J K}^{-1} \text{ mol}^{-1} \).

Two flasks \( \text{I} \) and \( \text{II} \) shown below are connected by a valve of negligible volume.

When the valve is opened, the final pressure of the system in bar is \( x \times 10^{-2} \). The value of \( x \) is _______. (Nearest integer)
[Assume : Ideal gas; \( 1 \, \text{bar} = 10^{5} \, \text{Pa} \); Molar mass of \( \mathrm{N}_2 = 28.0 \, \text{g mol}^{-1} \); \( R = 8.31 \, \text{J mol}^{-1} \text{K}^{-1} \)]

During which of the following processes, does entropy decrease ?
(A) Freezing of water to ice at \( 0^\circ\mathrm{C} \)
(B) Freezing of water to ice at \( -10^\circ\mathrm{C} \)
(C) \( \mathrm{N_2(g)} + 3\mathrm{H_2(g)} \rightarrow 2\mathrm{NH_3(g)} \)
(D) Adsorption of \( \mathrm{CO(g)} \) on lead surface
(E) Dissolution of \( \mathrm{NaCl} \) in water
Choose the correct answer from the options given below :

\( 200 \, \text{mL} \) of \( 0.2 \, \text{M} \) \( \mathrm{HCl} \) is mixed with \( 300 \, \text{mL} \) of \( 0.1 \, \text{M} \) \( \mathrm{NaOH} \). The molar heat of neutralization of this reaction is \( -57.1 \, \text{kJ} \). The increase in temperature in \( ^\circ \text{C} \) of the system on mixing is \( x \times 10^{-2} \). The value of \( x \) is ____________ (Nearest integer)
[Given: Specific heat of water \( = 4.18 \, \text{J} \, \text{g}^{-1} \text{K}^{-1} \), Density of water \( = 1.00 \, \text{g} \, \text{cm}^{-3} \)]
(Assume no volume change on mixing)

For water \( \Delta_{\text{vap}}H = 41 \, \text{kJ mol}^{-1} \) at \( 373 \, \text{K} \) and \( 1 \, \text{bar} \) pressure. Assuming that water vapour is an ideal gas that occupies a much larger volume than liquid water, the internal energy change during evaporation of water is ________ \( \text{kJ mol}^{-1} \).
[Use : \( R = 8.3 \, \text{J mol}^{-1} \, \text{K}^{-1} \).]