At a given temperature, what relationship appears to exist between a gas particle's mass and it speed?

How does graph change as particle mass increase?
Isra fills two identical balloons at identical temperatures. She fills one with O2 gas and the other with O3 gas. Which balloon will deflate faster? Why?
Conclusion
What can you conclude about gas molecule speeds in a container?

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Isra fills two identical balloons at identical temperatures. She fills one with O2 gas and the other with O3 gas. Which balloon will deflate faster? Why?

o2

To understand the relationship between a gas particle's mass and its speed at a given temperature, we can refer to the kinetic theory of gases. According to this theory, the average kinetic energy of gas particles is directly proportional to their temperature.

Now, because average kinetic energy depends on temperature and not mass, increasing the mass of a gas particle does not affect its speed at a given temperature. In other words, the relationship between mass and speed of gas particles remains constant regardless of changes in mass.

However, it's important to note that lighter gas particles, such as those with smaller masses, tend to move faster on average compared to heavier particles at the same temperature. This is because the overall kinetic energy is distributed among a greater number of lighter particles, resulting in higher speeds.

When it comes to graphing the relationship between particle mass and speed, there should be no change. This is because the mass of the particles does not influence their speed. So, a graph showing particle mass on the x-axis and speed on the y-axis would be a horizontal line, indicating a constant speed regardless of particle mass.

Moving on to the scenario with the two balloons filled by Isra, one with O2 gas and the other with O3 gas, we can determine which balloon will deflate faster by comparing their molecular masses.

O2 gas has a molecular mass of two oxygen atoms (16 + 16 = 32), while O3 gas has a molecular mass of three oxygen atoms (16 + 16 + 16 = 48). The O3 gas, being heavier, has slower-moving molecules compared to O2 gas. Therefore, the O3 balloon will deflate slower than the O2 balloon as its slower-moving gas molecules will escape at a slower rate.

In conclusion, based on the kinetic theory of gases, we can conclude that, on average, gas molecules in a container will have different speeds. Lighter gas particles generally have higher speeds compared to heavier particles at the same temperature. The relationship between particle mass and speed is that as mass increases, speed tends to decrease, but this relationship is due to the distribution of kinetic energy among particles and not directly influenced by mass.