Determine the speed of sound in oxygen using the following data. At STP ( T = 273 K and p = 1.0 10^5 N m ⁻² ), the mass of 22.4 litre of oxygen is 32 g . The molar heat capacity of oxygen is C_V = 2.5 R at constant volume and C_p = 3.5 R at constant pressure.

Step-by-step solution

The ratio of specific heats is = C_p C_V = 3.5 R 2.5 R = 1.4 The density of oxygen at STP is = M V = 32 10⁻³ kg 22.4 10⁻³ m ^3 = 10 7 kg m ⁻³ The speed of sound in a gas is given by Laplace's formula v = p Substituting the given values: v = 1.4 1.0 10^5 10/7 v = 1.4 0.7 10^5 v = 0.98 10^5 = 98000 v 313 m s ⁻¹