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A gas obeys the ideal-gas equation of state P V = N k T , where N = n NA is the number of molecules in the volume V at pressure P and temperature T and n is the number of gm-moles of the gas. Calculate the volume occupied by 1 gm·mole of the gas at atmospheric pressure and a temperature of 313.7 K . Avogadro’s constant is 6.02214 × 1023 mol−1 , Boltzmann’s constant is 1.38065 × 10−23 N · m/K , and 1 atm = 1.013 × 105 N/m2 . Answer in units of L.

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Answer:

The volume occupied is 25.7 L

Explanation:

Let's replace all the data in the formula

P . V = N . k . T

N = nNA

1 gm.mole . 6.02x10²³

k = Boltzmann's contant

T = T° in K

1 atm =  1.013 × 10⁵ N/m2

1.013 × 10⁵ N/m2 . Volume = 6.02x10²³  . 1.38065 × 10⁻²³ N · m/K . 313.7K

Volume = (6.02x10²³ . 1.38065 × 10⁻²³ N · m/K . 313.7K) / 1.013 × 10⁵ m2/N

Volume = 2607.32 N.m / 1.013 × 10⁵ m2/N = 0.0257 m³

1 dm³ = 1 L

1m³  = 1000 dm³

25.7 L

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