Question

at 25.0c helium molecules have an average velocity of 1.26x10^5 cm/s and methane molecukes have an average velocity of 6.30x10^4 cm/s calculate the kinetic energy of each type of molecule at 25.0c and determine which is greater

Answer 1

• Both average kinetic energies are equal to 3.18 × 10³ J/mol

Step-by-step explanation:

The average kinetic energy of gas particles depends only on the temperature. Thus you must expect that the average kinetic energies of both helium gas and methane gas at 25ºC are equal.

1. Kinetic energy of helium molecules

The mass of 1 mole of molecules of helium is 4 grams. Convert to kg, to use SI units: 0.004 kg

Convert the velocity to m/s: 1.26×10⁵ cm/s = 1.26 × 10³ m/s

`KE=(1)/(2)mv^2=(1)/(2)(0.004kg/mol)(1.26* 10^3m/s)=3.18* 10^3J/mol`

2. Kinetic energy of methane molecules

The mass of 1 mole of molecules of methade is 416 grams. Convert to kg, to use SI units: 0.016 kg

Convert the velocity to m/s: 6.30×10⁴ cm/s = 6.30 × 10⁴ m/s

`KE=(1)/(2)mv^2=(1)/(2)(0.016kg/mol)(6.30* 10^2m/s)=3.18* 10^3J/mol`

As expected both average kinetic energies are the same.