Question

the mass of a cubic metre of air at NTP is

Answer 1

The mass of a cubic metre of air at NTP is 1300g. hence correct option is (b).

We have to find the mass of one cubic metre of air at normal temperature and pressure (or NTP).

First we have to find the density of air at normal temperature and pressure.

We know, density of a gas is given by,

$\rho=\frac{PM}{RT}$

• ρ is density of gas
• P is pressure of gas
• M is molar mass of gas
• R is universal gas constant
• T is temperature in kelvin.

At normal temperature and pressure,

M = 29 g/mol = 0.029 kg/mol

P = 1.013 × 10⁵ N/m²

R = 8.314 J/K/mol

T = 273.15K

∴ ρ = (1.013 × 10⁵ × 0.029)/(8.314 × 273.15) ≈ 1.3 kg/m³

Now, mass = density × volume

= ρ × V

= 1.3 kg/m³ × 1 m³ [∵ volume of air, V = 1 m³ ]

= 1.3 kg = 1300 g

Therefore the mass of a cubic metre of air at NTP is 1300g.

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