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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 CH鈧�(g) and N鈧�(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 CH鈧�(g) and N鈧�(g) have an average kinetic energy of \(6.10 \times 10^{-21} J\). At 546 K, the average kinetic energy of both CH鈧�(g) and N鈧�(g) is \(1.22 \times 10^{-20} J\).

Step by step solution

01

Calculate the average kinetic energy of CH鈧�(g) at 273 K

To calculate the average kinetic energy of CH鈧�(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 N鈧�(g) at 273 K

Similarly, to calculate the average kinetic energy of N鈧�(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 CH鈧�(g) at 546 K

Next, calculate the average kinetic energy of CH鈧�(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 N鈧�(g) at 546 K

Finally, calculate the average kinetic energy of N鈧�(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 CH鈧�(g) and N鈧�(g) at 273 K and 546 K.

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Most popular questions from this chapter

Ethene is converted to ethane by the reaction $$ \mathrm{C}_{2} \mathrm{H}_{4}(g)+\mathrm{H}_{2}(g) \stackrel{\mathrm{Cindys}}{\longrightarrow} \mathrm{C}_{2} \mathrm{H}_{6}(g) $$ \(\mathrm{C}_{2} \mathrm{H}_{4}\) flows into a catalytic reactor at \(25.0 \mathrm{~atm}\) and \(300 .{ }^{\circ} \mathrm{C}\) with a flow rate of \(1000 .\) L/min. Hydrogen at \(25.0\) atm and \(300 .{ }^{\circ} \mathrm{C}\) flows into the reactor at a flow rate of \(1500 . \mathrm{L} / \mathrm{min}\). If \(15.0 \mathrm{~kg} \mathrm{C}_{2} \mathrm{H}_{6}\) is collected per minute, what is the percent yield of the reaction?

A compressed gas cylinder contains \(1.00 \times 10^{3} \mathrm{~g}\) argon gas. The pressure inside the cylinder is \(2050 .\) psi (pounds per square inch) at a temperature of \(18^{\circ} \mathrm{C}\). How much gas remains in the cylinder if the pressure is decreased to \(650 .\) psi at a temperature of \(26^{\circ} \mathrm{C} ?\)

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Consider three identical flasks filled with different gases. Flask A: \(\mathrm{CO}\) at 760 torr and \(0^{\circ} \mathrm{C}\) Flask B: \(\mathrm{N}_{2}\) at 250 torr and \(0^{\circ} \mathrm{C}\) Flask C: \(\mathrm{H}_{2}\) at 100 torr and \(0^{\circ} \mathrm{C}\) a. In which flask will the molecules have the greatest average kinetic energy? b. In which flask will the molecules have the greatest average velocity?

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