Thermodynamics - Kinetic energy in a compound

[steve233]

Homework Statement

In a compound made up of 35% nitrogen, 60% oxygen and 5% water vapor, which of the components has the most kinetic energy in Joules? Assume room temperature (300K) and atmospheric pressure. Volume of room is 1000m^3

Homework Equations

1/2mv²
1/2kT
v_rms = root(3kT/m)
PV = NkT

The Attempt at a Solution

My idea was to take just 1 moles worth of the compound and add 35% more to that number (for nitrogen, for example), but this doesn't seem correct. I'm not sure how to incorporate the percentages in with the kinetic energy of the compound. I'm not much of a chemist so this could be my problem. Any hints or tips would be very helpful. Thanks

 

[mark726]

!

it is important to approach this problem systematically and use the appropriate equations to solve it. The first thing to note is that kinetic energy is directly related to the velocity of the particles in a substance. So, to find the component with the most kinetic energy, we need to find the component with the highest velocity.

To do this, we can use the equation vrms = root(3kT/m), where vrms is the root mean square velocity, k is the Boltzmann constant, T is temperature in Kelvin, and m is the mass of the particle. We can plug in the values for temperature and atmospheric pressure (which is equivalent to 1 mole of gas at standard temperature and pressure) to find the vrms for each component.

For nitrogen: vrms = √(3 * 1.38x10^-23 * 300 / 0.028) = 505.9 m/s
For oxygen: vrms = √(3 * 1.38x10^-23 * 300 / 0.032) = 487.8 m/s
For water vapor: vrms = √(3 * 1.38x10^-23 * 300 / 0.018) = 636.4 m/s

From this, we can see that water vapor has the highest vrms and therefore the most kinetic energy in Joules. To find the total kinetic energy, we can use the equation KE = 1/2mv^2, where m is the mass of the particle and v is the velocity. We can then use the mass percentage of each component to calculate the total kinetic energy for the whole compound.

For nitrogen: KE = 1/2 * (0.35 * 1000) * (505.9)^2 = 44,992,075 Joules
For oxygen: KE = 1/2 * (0.60 * 1000) * (487.8)^2 = 71,300,160 Joules
For water vapor: KE = 1/2 * (0.05 * 1000) * (636.4)^2 = 20,306,610 Joules

Therefore, the oxygen component has the most kinetic energy in the compound.