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Mechanical Properties Of Fluids

Question

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Molar volume is the volume occupied by 1 mol of any (ideal) gas at standard temperature and pressure (STP: 1 atmospheric pressure, 0 °C). Show that it is 22.4 litres.

Solution

The ideal gas equation relating pressure (P), volume (V), and absolute temperature (T) is given as,
PV = nRT

where,
R is the universal gas constant = 8.314 J mol^–1 K^–1
n = Number of moles = 1
T = Standard temperature = 273 K
P = Standard pressure = 1 atm = 1.013 × 10⁵ Nm^–2
∴ V =

nRT over straight P

= 1 × 8.314 × 273 / (1.013 × 10⁵)
= 0.0224 m³
= 22.4 litres
Hence, the molar volume of a gas at STP is 22.4 litres.

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