Specific heat of one mole of hydrogen at constant pressure and at constant volume are 450 $J K^{- 1}$ and 300 $J K^{- 1}$ respectively. Then what is the density of the gas at S.T.P ?
$(P_{a t m} = 1.013 \times 10^{5} {N m}^{- 2})$

2.47 k g / m^{3}

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3.0 k g / m^{3}

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3.58 k g / m^{3}

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4.0 k g / m^{3}

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No solution

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Solution

The correct option is E No solution
Let the density be $x g / c m^{3}$ .

So, volume of $x$ gm of $H_{2}$ at STP is $1000 c m^{3}$ .

Therefore, volume of one mole ( $2.016 g m$ ) of gas $= \frac{1000}{x} \times 2.016 {c m}^{3}$

$\Rightarrow C_{P} - C_{V} = R = \frac{P V}{T}$

$\Rightarrow 150 = \frac{1.013 \times 10^{5} \times 1000 \times 2.016 \times 10^{- 3}}{x \times 273}$

$\Rightarrow x = 4.99 k g / m^{3}$

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Specific heat of one mole of hydrogen at constant pressure and at constant volume are 450 JK−1 and 300 JK−1 respectively. Then what is the density of the gas at S.T.P ? (Patm=1.013×105Nm−2)

The correct option is E No solutionLet the density be x g/cm3.So, volume of x gm of H2 at STP is 1000 cm3.Therefore, volume of one mole (2.016 gm) of gas =1000x×2.016 cm3⇒CP−CV=R=PVT⇒150=1.013×105×1000×2.016×10−3x×273⇒x=4.99 kg/m3

Specific heat of one mole of hydrogen at constant pressure and at constant volume are 450 $J K^{- 1}$ and 300 $J K^{- 1}$ respectively. Then what is the density of the gas at S.T.P ?
$(P_{a t m} = 1.013 \times 10^{5} {N m}^{- 2})$