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Chapter 5: Problem 70

As we know, UF \(_{6}\) is a much heavier gas than helium. Yet at a given temperature, the average kinetic energies of the samples of the two gases are the same. Explain.

Short Answer

Expert verified
At a given temperature, both UF\(_{6}\) and helium will have the same average kinetic energy, despite UF\(_{6}\) being heavier, because according to the kinetic theory of gases, kinetic energy of gases depends only on temperature and it is same for all gas molecules at a particular temperature.

Step by step solution

01

Understand the Kinetic Theory of Gases

The kinetic theory of gases explains a number of properties of gases by assuming that gases are composed of very small particles in constant, random motion. The key insight from this theory relevant to this problem is the idea that the average kinetic energy of a gas is directly proportional to its temperature, not its mass. This means that for any two gases at the same temperature, the average kinetic energy of the gas particles in each case will be the same. This explains why UF\(_{6}\) and helium, despite the heavier mass of UF\(_{6}\), have the same average kinetic energy at a given temperature.
02

Discuss how Mass doesn't affect Average Kinetic Energy

Though UF\(_{6}\) is heavier than helium, the average kinetic energy of the two gases at a given temperature is the same because kinetic energy depends on temperature and not on the mass of the gas. The mass of the molecular gas affects the speed of particles, with lighter particles generally moving faster than heavier ones, but does not affect the kinetic energy. So, irrespective of the mass, the kinetic energy of all molecular gases is nearly the same at a particular temperature.

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Most popular questions from this chapter

List the characteristics of an ideal gas.

Write the expression for the root-mean-square speed for a gas at temperature \(T\). Define each term in the equation and show the units that are used in the calculations

The temperature of \(2.5 \mathrm{~L}\) of a gas initially at STP is increased to \(250^{\circ} \mathrm{C}\) at constant volume. Calculate the final pressure of the gas in atm.

Some commercial drain cleaners contain two components: sodium hydroxide and aluminum powder. When the mixture is poured down a clogged drain, the following reaction occurs: $$2 \mathrm{NaOH}(a q)+2 \mathrm{Al}(s)+6 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow_{2 \mathrm{NaAl}(\mathrm{OH})_{4}(a q)+3 \mathrm{H}_{2}(g)}$$ The heat generated in this reaction helps melt away obstructions such as grease, and the hydrogen gas released stirs up the solids clogging the drain. Calculate the volume of \(\mathrm{H}_{2}\) formed at STP if \(3.12 \mathrm{~g}\) of \(\mathrm{Al}\) is treated with an excess of \(\mathrm{NaOH}\).

A gas at \(772 \mathrm{mmHg}\) and \(35.0^{\circ} \mathrm{C}\) occupies a volume of \(6.85 \mathrm{~L}\). Calculate its volume at STP.
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