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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

1 .00 mol of molecular nitrogen gas expands in volume very quickly, so no heat is exchanged with the environment during the process. If the volume increases from \(1.00 \mathrm{~L}\) to \(1.50 \mathrm{~L},\) determine the work done on the environment if the gas's temperature dropped from \(22.0^{\circ} \mathrm{C}\) to \(18.0^{\circ} \mathrm{C}\). Assume ideal gas behavior.

Air at 1.00 atm is inside a cylinder \(20.0 \mathrm{~cm}\) in radius and \(20.0 \mathrm{~cm}\) in length that sits on a table. The top of the cylinder is sealed with a movable piston. A \(20.0-\mathrm{kg}\) block is dropped onto the piston. From what height above the piston must the block be dropped to compress the piston by \(1.00 \mathrm{~mm} ? 2.00 \mathrm{~mm} ? 1.00 \mathrm{~cm} ?\)

Molar specific heat at constant pressure, \(C_{p}\), is larger than molar specific heat at constant volume, \(C_{V}\), for a) a monoatomic ideal gas. b) a diatomic atomic gas. c) all of the above. d) none of the above.

Treating air as an ideal gas of diatomic molecules, calculate how much heat is required to raise the temperature of the air in an \(8.00 \mathrm{~m}\) by \(10.0 \mathrm{~m}\) by \(3.00 \mathrm{~m}\) room from \(20.0^{\circ} \mathrm{C}\) to \(22.0^{\circ} \mathrm{C}\) at \(101 \mathrm{kPa}\). Neglect the change in the number of moles of air in the room.

A tire on a car is inflated to a gauge pressure of \(32 \mathrm{lb} / \mathrm{in}^{2}\) at a temperature of \(27^{\circ} \mathrm{C}\). After the car is driven for \(30 \mathrm{mi}\), the pressure has increased to \(34 \mathrm{lb} / \mathrm{in}^{2} .\) What is the temperature of the air inside the tire at this point? a) \(40^{\circ} \mathrm{C}\) b) \(23^{\circ} \mathrm{C}\) c) \(32^{\circ} \mathrm{C}\) d) \(54^{\circ} \mathrm{C}\)
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