Which factor: T or p, will affect the number of molecular collisions, most significantly?
Answer:
The root mean square velocity of a gas is (3RT/M)^0.5. From this, you can see that doubling the temperature would only increase the RMS velocity by a factor of 1.4. To reconcile this with Gay-Lussac's law (P-T relationship), remember that the average kinetic energy of the gas will go up by a factor of 2, making the pressure double as expected (pressure is, after all, just a measure of the force exerted by a gas).
This gives you all you need for your answer. Doubling the pressure of a system but keeping the temperature constant will double the frequency of collisions because you are simply putting twice as many molecules in the same space. This isn't the case with doubling the temperature, since you're not also doubling the velocity of the gas particles, just their kinetic energy.
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