Heat $$Q=32RT$$, is supplied to moles of an ideal diatomic gas at temperature $$7$$, which remains constant. How many moles of the gas are dissolved into atoms?

Question

Heat $$Q=32RT$$, is supplied to moles of an ideal diatomic gas at temperature $$7$$, which remains constant. How many moles of the gas are dissolved into atoms?

Infinity Learn · Accepted Answer

Let x moles of diatomic gas be associated, x moles of diatomic gas become 2x moles of a monoatomic gas after dissociation. Internal energy of n moles of an ideal gas

$\begin{array}{l} = \frac{3}{2} nRT for monoatomic gas \\ = \frac{5}{2} nRT for diatomic gas \end{array}$

So, (Internal energy of 2x moles of a monoatomic gas + internal energy of (4 - x) moles of a diatomic gas) - internal energy of 4 moles of a diatomic gas

$\begin{array}{l} = \frac{3}{2} RT (given) \\ (2 x) (\frac{3 RT}{2}) + (4 - x) (\frac{5}{2} RT) - (4) (\frac{5}{2} RT) = \frac{3}{2} RT \end{array}$

On solving, x = 3 moles.

Internal energy

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Heat $Q = \frac{3}{2} RT$ , is supplied to moles of an ideal diatomic gas at temperature 7, which remains constant. How many moles of the gas are dissolved into atoms?

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Internal energy

Remember concepts with our Masterclasses.

Heat Q=32RT, is supplied to moles of an ideal diatomic gas at temperature 7, which remains constant. How many moles of the gas are dissolved into atoms?

Ready to Test Your Skills?

free study material

Heat $Q = \frac{3}{2} RT$ , is supplied to moles of an ideal diatomic gas at temperature 7, which remains constant. How many moles of the gas are dissolved into atoms?