Question

A gas bulb of 1 ltr. capacity contains 2.0x1021 nitrogen molecules exerting a

pressure of 7.57x103Nm-2. Calculate the temperature of gas molecules.
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Answer 1

Given info : A gas bulb of 1 litre capacity contains 2 × 10²¹ nitrogen molecules exerting a pressure 7.57 × 10³ N/m².

To find : the temperature of gas molecules is...

solution : no of nitrogen molecules = 2 × 10²¹

no of moles of nitrogen = no of nitrogen molecules/Avogadro's number

= 2 × 10²¹/6.023 × 10²³

= 2/602.3

= 0.00332 mol

we know, PV = nRT [ from an ideal gas equation ]

here n = 0.00332 mol

R = universal gas constant = 0.082 litre.atm/mol/k

T = ?

P = 7.57 × 10³ N/m² = (7.57 × 10³/1.013 × 10⁵) atm

= 7.472 × 10¯² atm = 0.07472 atm

V = 1 litre

now, 0.07472 × 1 = 0.00332 × 0.082 × T

⇒T = 274.46 K

Therefore the temperature of gas molecules is 274.46 K.

[ note : if answer is in °C , just use K = 273 + C , and find the temperature in °C ]