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For the response

    \[\begin{array}{*{35}{l}} 2A\left( g \right)\text{ }+\text{ }B\left( g \right)\text{ }\to \text{ }2D\left( g \right) \\ ~ \\ U\theta \text{ }=\text{ }\text{ }10.5\text{ }kJ\text{ }and\text{ }S\theta \text{ }=\text{ }\text{ }44.1\text{ }JK1\text{ }. \\ \end{array}\]

Compute ∆Gθ for the response, and anticipate whether the response might happen suddenly.
CBSE | Chemistry | Class 11 | Exercise 1 | NCERT | Thermodynamics
For the response

    \[\begin{array}{*{35}{l}} 2A\left( g \right)\text{ }+\text{ }B\left( g \right)\text{ }\to \text{ }2D\left( g \right) \\ ~ \\ U\theta \text{ }=\text{ }\text{ }10.5\text{ }kJ\text{ }and\text{ }S\theta \text{ }=\text{ }\text{ }44.1\text{ }JK1\text{ }. \\ \end{array}\]

Compute ∆Gθ for the response, and anticipate whether the response might happen suddenly.

Solution:

For the given response,

 

    \[\begin{array}{*{35}{l}} 2\text{ }A\left( g \right)\text{ }+\text{ }B\left( g \right)\text{ }\to \text{ }2D\left( g \right) \\ ~ \\ ng\text{ }=\text{ }2\text{ }\text{ }\left( 3 \right)\text{ }=\text{ }\text{ }1\text{ }mole \\ \end{array}\]

Subbing the worth of ∆Uθ in the declaration of ∆H:

 

    \[\begin{array}{*{35}{l}} H\theta \text{ }=\text{ }U\theta \text{ }+\text{ }ngRT \\ ~ \\ =\text{ }\left( \text{ }10.5\text{ }kJ \right)\text{ }\text{ }\left( \text{ }1 \right)\text{ }\left( 8.314\text{ }\times \text{ }103\text{ }kJ\text{ }K1\text{ }mol1\text{ } \right)\text{ }\left( 298\text{ }K \right) \\ ~ \\ =\text{ }\text{ }10.5\text{ }kJ\text{ }\text{ }2.48\text{ }kJ\text{ }H\theta \text{ }=\text{ }\text{ }12.98\text{ }kJ \\ \end{array}\]

Subbing the upsides of ∆Hθ and ∆Sθ in the declaration of ∆Gθ :

 

    \[\begin{array}{*{35}{l}} G\theta \text{ }=\text{ }H\theta \text{ }\text{ }TS\theta \\ ~ \\ =\text{ }\text{ }12.98\text{ }kJ\text{ }\text{ }\left( 298\text{ }K \right)\text{ }\left( \text{ }44.1\text{ }J\text{ }K1\text{ } \right) \\ ~ \\ =\text{ }\text{ }12.98\text{ }kJ\text{ }+\text{ }13.14\text{ }kJ \\ ~ \\ G\theta \text{ }=\text{ }+\text{ }0.16\text{ }kJ \\ \end{array}\]

Since ∆Gθ for the response is positive, the response won’t happen unexpectedly.

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