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The pressure-volume work for an ideal gas can be calculated by using the expression w = `- int_(v_i)^(v_f) p_(ex) dV`. The work can also be calculated from the pV– plot by using the area under the curve within the specified limits. When an ideal gas is compressed (a) reversibly or (b) irreversibly from volume Vi to Vf. choose the correct option.
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For an ideal gas, the work of reversible expansion under isothermal condition can be calculated by using the expression w = `- nRT` In `V_f/V_i`. A sample containing 1.0 mol of an ideal gas is expanded isothermally and reversibly to ten times of its original volume, in two separate experiments. The expansion is carried out at 300 K and at 600 K respectively.
(i) Work done at 600 K is 20 times the work done at 300 K.
(ii) Work done at 300 K is twice the work done at 600 K.
(iii) Work done at 600 K is twice the work done at 300 K.
(iv) ∆U = 0 in both cases.
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A sample of 1.0 mol of a monoatomic ideal gas is taken through a cyclic process of expansion and compression as shown in figure 6.1. What will be the value of ∆H for the cycle as a whole?
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Expansion of a gas in vacuum is called free expansion. Calculate the work done and the change in internal energy when 1 litre of ideal gas expands isothermally into vacuum until its total volume is 5 litre?
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What will be the work done on an ideal gas enclosed in a cylinder, when it is compressed by a constant external pressure, pext in a single step as shown in figure. Explain graphically.
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How will you calculate work done on an ideal gas in a compression, when change in pressure is carried out in infinite steps?
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Represent the potential energy/enthalpy change in the following processes graphically.
(a) Throwing a stone from the ground to roof.
(b) \[\ce{1/2 H2(g) + 1/2 Cl2 (g) ⇌ HCl (g) Δ_rH^Θ = - 92.32 kJ mol^{-1}}\]
In which of the processes potential energy/enthalpy change is contributing factor to the spontaneity?
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1.0 mol of a monoatomic ideal gas is expanded from state (1) to state (2) as shown in figure. Calculate the work done for the expansion of gas from state (1) to state (2) at 298 K.
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An ideal gas is allowed to expand against a constant pressure of 2 bar from 10 L to 50 L in one step. Calculate the amount of work done by the gas. If the same expansion were carried out reversibly, will the work done be higher or lower than the earlier case? (Given that 1 L bar = 100 J)
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Match the following :
| A | B |
| (i) Adiabatic process | (a) Heat |
| (ii) Isolated system | (b) At constant volume |
| (iii) Isothermal change | (c) First law of thermodynamics |
| (iv) Path function | (d) No exchange of energy and matter |
| (v) State function | (e) No transfer of heat |
| (vi) ΔU = q | (f) Constant temperature |
| (vii) Law of conservation of energy | (g) Internal energy |
| (viii) Reversible process | (h) Pext = o |
| (ix) Free expansion | (i) At constant pressure |
| (x) ΔH = q | (j) Infinitely slow process which proceeds through a series of equilibrium states. |
| (xi) Intensive property | (k) Entropy |
| (xii) Extensive property | (l) Pressure |
| (m) Specific heat |
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Match the following :
| Column I | Column II |
| (i) Entropy of vapourisation | (a) decreases |
| (ii) K for spontaneous process | (b) is always positive |
| (iii) Crystalline solid state | (c) lowest entropy |
| (iv) ∆U in adiabatic expansion of ideal gas | (d) `(∆H_(vap))/T_b` |
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Graphically show the total work done in an expansion when the state of an ideal gas is changed reversibly and isothermally from \[\ce{(p_i, V_i)}\] to \[\ce{(p_f , V_f )}\]. With the help of a pV plot compare the work done in the above case with that carried out against a constant external pressure \[\ce{p_f}\].
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Write balanced chemical equation for the following reactions:
Permanganate ion \[\ce{(MnO^{-}4)}\] reacts with sulphur dioxide gas in acidic medium to produce \[\ce{Mn^{2+}}\] and hydrogen sulphate ion.
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Write balanced chemical equation for the following reactions:
Reaction of liquid hydrazine \[\ce{(N2H4)}\] with chlorate ion \[\ce{(ClO^{-}3)}\] in basic medium produces nitric oxide gas and chloride ion in gaseous state.
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Write balanced chemical equation for the following reactions:
Dichlorine heptaoxide \[\ce{(Cl2O7)}\] in gaseous state combines with an aqueous solution of hydrogen peroxide in acidic medium to give chlorite ion \[\ce{(ClO^{-}2)}\] and oxygen gas. (Balance by ion-electron method)
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Balance the following equations by the oxidation number method.
\[\ce{Fe^{2+} + H^{+} + Cr2O^{2-}7 -> Cr^{3+} + Fe^{3+} + H2O}\]
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Balance the following equations by the oxidation number method.
\[\ce{I2 + NO^{-}3 -> NO2 + IO^{-}3}\]
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Balance the following equations by the oxidation number method.
\[\ce{I2 + S2O^{2-}3 -> I- + S4O^{2-}6}\]
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Balance the following equations by the oxidation number method.
\[\ce{MnO2 + C2O^{2-}4 -> Mn^{2+} + CO2}\]
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Identify the redox reactions out of the following reactions and identify the oxidising and reducing agents in them.
\[\ce{3HCl (aq) + HNO3 (aq) -> Cl2 (g) + NOCl (g) + 2H2O (l)}\]
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