2 moles of ideal gas expand isothermally and reversibly

Asked by admin @ 13/08/2021 in Chemistry viewed by 336 People

Two moles of an ideal gas is expanded isothermally and reversibly from 1 litre to 10 litre at 300 K . The enthalpy change (in kJ) for the process is:

a) 11.4 kJ
b) -11.4 kJ
c) 0 kJ
d) 4.8 kJ

Answered by admin @ 13/08/2021

Given conditions,

No. of moles(n) = 2 moles.

Temperature(T) = 300 K.

V₂ = 10 L, and V₁ = 1 L.

Universal Gas Constant (R) = 8.31 J/moleK.

Using the formula,

Work done = -2.303nRTlog(V₂/V₁) [For Chemistry.]

∴ Work done = -2.303 × 2 × 8.31 × 300 × log(10/1)

∴ Work done = -11482.758 J.

∴ Work done = -11.483 kJ.

Now, Process is Isothermal, therefore, Internal Energy will also be zero.

Thus, Using first Law of thermodynamics (of Chemistry and not of physics)

∴ ΔU = ΔQ + w

∴ ΔQ = - w

∴ ΔQ = - (-11.483)

∴ ΔQ = 11.483 kJ ≈ 11.4 kJ.

Now, ΔQ is the enthaly because heat constant at constant pressure is enthalpy.

Hence, Option (a). is true.

Hope it helps.

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