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Entropy Change in Isothermal Process

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Question

In a container 5 moles of $H e$ gas are mixed with 4 moles of $H_{2}$ gas isothermally. Find out the entropy change in mixing for the system in $J K^{- 1}$ , given that $R = 8.314 J m o l^{- 1} K^{- 1}$

20.89

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51.04

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98.88

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-66.89

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Solution

The correct option is B 51.04
Entropy change due to Isothermal Mixing : Due to mixing of gases, entropy of the system Changes. Initially both the gases have the same temperature so mixing will not change the temperature. Isothermal mixing increases the entropy of the system.
$Δ S_{s y s t e m (m i x i n g)} = Δ S_{G a s 1 (d u e t o m i x i n g)} + Δ S_{G a s 2 (d u e t o m i x i n g)}$

$Δ S_{s y s} = - n_{1} R l n (χ_{1}) - n_{2} R l n (χ_{2}) Δ S_{s y s} = - R [n_{1} l n (χ_{1}) + n_{2} l n (χ_{2})]$

$1 = H e; 2 = H_{2}$

$χ_{1} = \frac{5}{5 + 4} = \frac{5}{9}; χ_{2} = \frac{4}{5 + 4} = \frac{4}{9} Δ S = - 8.314 [5 \times l n (\frac{5}{9}) + 4 \times l n \frac{4}{9})] Δ S = 51.04 J K^{- 1}$

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Similar questions

Q. In a container 5 moles of

H e

gas are mixed with 4 moles of

H_{2}

gas isothermally. Find out the entropy change in mixing for the system in

J K^{- 1}

, given that

R = 8.314 J m o l^{- 1} K^{- 1}

Q. Consider an isothermal reversible compression of 1 mole of an ideal gas in which pressure of the system increased from 5 atm to 30 atm at 300 K. The entropy change (in kJ) of the surrounding is:
(

R = 8.314 J m o l^{- 1} K^{- 1}

)

Q. The molar entropy content of 1 mole of oxygen

(O_{2})

gas at 300 K and 1 atm is

250 J m o l^{- 1} K^{- 1} .

Calculate

△ G

when 1 mole of oxygen is expanded reversibly and isothermally from 300 K, 1 atm to double its volume (Take

R = 8.314 J m o l^{- 1} K^{- 1}, l o g e = 2.303)

Q. Two moles of an ideal gas

(C_{v, m} = 12.5 J K^{- 1} m o l^{- 1})

are at

300 K

and

5 d m^{3}

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600 K

and the volume changed to

10 d m^{3}

, calculate the entropy change.
(take ln2=0.7,

R = 8.3 J m o l^{- 1} K^{- 1}

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The entropy change involved in the isothermal reversible expansion of 2 mole of an ideal gas from a volume of $10 d m^{3}$ to a volume of $100 d m^{3}$ at $27^{\circ} C$ is :

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Entropy Change in Isothermal Process

Standard XIII Chemistry

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In a container 5 moles of He gas are mixed with 4 moles of H2 gas isothermally. Find out the entropy change in mixing for the system in J K−1, given that R=8.314 J mol−1 K−1

In a container 5 moles of $H e$ gas are mixed with 4 moles of $H_{2}$ gas isothermally. Find out the entropy change in mixing for the system in $J K^{- 1}$ , given that $R = 8.314 J m o l^{- 1} K^{- 1}$