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Chapter 5: Problem 95

Calculate the average kinetic energies of \(\mathrm{CH}_{4}(g)\) and \(\mathrm{N}_{2}(g)\) molecules at \(273 \mathrm{~K}\) and \(546 \mathrm{~K}\).

Short Answer

Expert verified
The average kinetic energies of CH₄(g) and N₂(g) at 273 K and 546 K can be calculated using the formula \(K.E. = \dfrac{3}{2} kT \), where k is Boltzmann's constant (\(1.38 \times 10^{-23} JK^{-1}\)). At 273 K, both CH₄(g) and N₂(g) have an average kinetic energy of \(6.10 \times 10^{-21} J\). At 546 K, the average kinetic energy of both CH₄(g) and N₂(g) is \(1.22 \times 10^{-20} J\).

Step by step solution

01

Calculate the average kinetic energy of CH₄(g) at 273 K

To calculate the average kinetic energy of CH₄(g) at 273 K, we need to use the formula mentioned above and plug in the known values: \(K.E. = \dfrac{3}{2} kT\) \(K.E. = \dfrac{3}{2} (1.38 \times 10^{-23} J K^{-1})(273 K)\) Now, perform the calculation to find the average kinetic energy.
02

Calculate the average kinetic energy of N₂(g) at 273 K

Similarly, to calculate the average kinetic energy of N₂(g) at 273 K, use the formula and plug in the known values: \(K.E. = \dfrac{3}{2} kT\) \(K.E. = \dfrac{3}{2} (1.38 \times 10^{-23} J K^{-1})(273 K)\) Perform the calculation to find the average kinetic energy.
03

Calculate the average kinetic energy of CH₄(g) at 546 K

Next, calculate the average kinetic energy of CH₄(g) at 546 K using the formula and known values: \(K.E. = \dfrac{3}{2} kT\) \(K.E. = \dfrac{3}{2} (1.38 \times 10^{-23} J K^{-1})(546 K)\) Perform the calculation to find the average kinetic energy.
04

Calculate the average kinetic energy of N₂(g) at 546 K

Finally, calculate the average kinetic energy of N₂(g) at 546 K using the formula and known values: \(K.E. = \dfrac{3}{2} kT\) \(K.E. = \dfrac{3}{2} (1.38 \times 10^{-23} J K^{-1})(546 K)\) Perform the calculation to find the average kinetic energy. After completing steps 1-4, you will have the average kinetic energies of CH₄(g) and N₂(g) at 273 K and 546 K.

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Most popular questions from this chapter

Consider two different containers, each filled with 2 moles of \(\mathrm{Ne}(\mathrm{g}) .\) One of the containers is rigid and has constant volume. The other container is flexible (like a balloon) and is capable of changing its volume to keep the external pressure and internal pressure equal to each other. If you raise the temperature in both containers, what happens to the pressure and density of the gas inside each container? Assume a constant external pressure.

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