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Chapter 19: Problem 10

Compare the average kinetic energy at room temperature of a nitrogen molecule to that of a nitrogen atom. Which has the larger kinetic energy? a) nitrogen atom b) nitrogen molecule c) They have the same energy. d) It depends upon the pressure.

Short Answer

Expert verified
Answer: c) They have the same energy.

Step by step solution

01

Calculate average kinetic energy at room temperature

Average kinetic energy (K.E.) of gas particles can be calculated using the formula: K.E. = (3/2)kT where k is the Boltzmann constant (1.38 x 10^{-23} J/K) and T is the temperature in kelvins. At room temperature (approximately 25°C), the temperature in kelvins is T = 25 + 273.15 = 298.15 K.
02

Compare the average kinetic energy of nitrogen atom and nitrogen molecule

We know that at the same temperature, all gas particles have the same average kinetic energy. Therefore, we don't need to calculate the average kinetic energy of nitrogen atom and nitrogen molecule separately, as they will have the same kinetic energy at the same temperature.
03

Determine which has the larger kinetic energy

Since the average kinetic energy of nitrogen atom and nitrogen molecule is the same at room temperature, the correct answer is: c) They have the same energy.

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Most popular questions from this chapter

Chapter 13 examined the variation of pressure with altitude in the Earth's atmosphere, assuming constant temperature-a model known as the isothermal atmosphere. A better approximation is to treat the pressure variations with altitude as adiabatic. Assume that air can be treated as a diatomic ideal gas with effective molar mass \(M_{\text {air }}=28.97 \mathrm{~g} / \mathrm{mol}\) a) Find the air pressure and temperature of the atmosphere as functions of altitude. Let the pressure at sea level be \(p_{0}=101.0 \mathrm{kPa}\) and the temperature at sea level be \(20.0^{\circ} \mathrm{C}\) b) Determine the altitude at which the air pressure and density are half their sea-level values. What is the temperature at this altitude, in this model? c) Compare these results with the isothermal model of Chapter \(13 .\)

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