Question

chemwork consider separate 1.0-l gaseous samples of ch₄, o₂, and ar, all at stp and all acting ideally. rank the gases in order of increasing average kinetic energy. \\( \bigcirc \\ ch_4 = o_2 = ar \\) \\( \bigcirc \\ o_2 < ch_4 < ar \\) \\( \bigcirc \\ ar < o_2 < ch_4 \\) \\( \bigcirc \\ ch_4 < o_2 < ar \\)

Explanation:

Step1: Recall Kinetic Energy Formula

The average kinetic energy (\(KE_{avg}\)) of a gas is given by \(KE_{avg} = \frac{3}{2}kT\), where \(k\) is Boltzmann's constant and \(T\) is temperature in Kelvin.

Step2: Analyze Temperature Condition

All gases (\(CH_4\), \(O_2\), \(Ar\)) are at STP, so they have the same temperature (\(T\)).

Step3: Determine Kinetic Energy Relationship

Since \(KE_{avg}\) depends only on \(T\) (and \(k\) is constant), gases at the same temperature have the same average kinetic energy.

Answer:

\(CH_4 = O_2 = Ar\) (the first option: \(CH_4 = O_2 = Ar\))