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.

Question

Chemistry

Colin

Yesterday, 23:12

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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Answers (1)

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Irvin Villarreal · Answer 1

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