Question

What is the kinetic energy of a mole of oxygen molecules travelling at 255 m/s?

Answer 1

The kinetic energy is 1.041 kJ.

Explanation:

The mass of 1 oxygen molecule is

`1 cancel("O₂ molecule") × (32.00 cancel("u"))/(1 cancel("O₂ molecule")) × (1.661 × 10^"-27"color(white)(l) "kg")/(1 cancel("u")) = 5.315 × 10^"-26"color(white)(l) "kg"`

The formula for kinetic energy is

`KE = ½mv^2`

The kinetic energy of 1 molecule is

`KE = ½ × 5.315 × 10^"-26"color(white)(l) "kg" × ("255 m·s"^"-1")^2 = 1.728 × 10^"-21" cancel("kg·m⁻²s⁻²") × "1 J"/(1 cancel("kg·m⁻²s⁻²")) = 1.728 × 10^-21color(white)(l) "J"`

For 1 mole of O₂ molecules, the kinetic energy is

`6.022 × 10^23 cancel("molecules") × (1.728 × 10^"-21"color(white)(l) "J")/(1 cancel("molecule")) = "1041 J" = "1.041 kJ"`