Ch.10 - Gases: Their Properties & Behavior

McMurry8th EditionChemistryISBN: 9781292336145Not the one you use?Change textbook

McMurry 8th Edition

Ch.10 - Gases: Their Properties & Behavior

Problem 11

Chapter 10, Problem 11

The coldest temperature recorded at ground level on Earth was -89.2 °C at the Vostok Station in Antarctica. What is the speed of a nitrogen molecule at this temperature? (LO 10.9)(a) 933 m/s (b) 40.2 m/s(c) 404 m/s (d) 12.8 m/s

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Identify the formula for the root-mean-square speed of a gas molecule: \( v_{rms} = \sqrt{\frac{3kT}{m}} \), where \( k \) is the Boltzmann constant, \( T \) is the temperature in Kelvin, and \( m \) is the mass of a nitrogen molecule.

Convert the given temperature from Celsius to Kelvin using the formula: \( T(K) = T(°C) + 273.15 \).

Calculate the mass of a nitrogen molecule. First, find the molar mass of nitrogen (N2), which is approximately 28.02 g/mol. Convert this to kilograms per molecule by dividing by Avogadro's number (\( 6.022 \times 10^{23} \) molecules/mol) and converting grams to kilograms.

Substitute the values for \( k \), \( T \), and \( m \) into the root-mean-square speed formula to find \( v_{rms} \).

Compare the calculated \( v_{rms} \) with the given options to determine the correct answer.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Kinetic Molecular Theory

The Kinetic Molecular Theory explains the behavior of gases in terms of particles in constant motion. It posits that gas molecules move rapidly and randomly, and their speed is influenced by temperature. As temperature decreases, the average kinetic energy of the molecules also decreases, leading to slower molecular speeds.

Root Mean Square Speed

Root Mean Square Speed (RMS speed) is a statistical measure of the speed of particles in a gas. It is calculated using the formula v_rms = sqrt(3RT/M), where R is the ideal gas constant, T is the absolute temperature in Kelvin, and M is the molar mass of the gas. This concept is crucial for determining the average speed of gas molecules at a given temperature.

Temperature Conversion

Temperature conversion is essential for solving problems involving temperature in different units. In this case, the temperature must be converted from Celsius to Kelvin by adding 273.15. This conversion is necessary because gas laws and kinetic energy calculations require absolute temperature measurements to ensure accuracy in the results.

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Textbook Question

An unknown gas is found to diffuse through a porous membrane 2.92 times more slowly than H2. What is the molecular weight of the gas? (a) 17.0 g/mol (b) 5.84 g/mol (c) 8.52 g/mol

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Textbook Question

A mixture of chlorine, hydrogen, and oxygen gas is in a container at STP. Which curve represents oxygen gas? (LO 10.8) (a) Curve (a) (b) Curve (b) (c) Curve (c)

Textbook Question

Two identical 732.0-L tanks each contain 212.0 g of gas at 293 K, with neon in one tank and nitrogen in the other. Based on the assumptions of kinetic–molecular theory, rank the gases from low to high for each of the following properties.

(a) Average speed

Textbook Question

Two 112-L tanks are filled with gas at 330 K. One contains 5.00 mol of Kr, and the other contains 5.00 mol of O₂. Considering the assumptions of kinetic–molecular theory, rank the gases from low to high for each of the following properties.

Textbook Question

Identify the true statement about deviations from ideal gas behavior. (LO 10.12) (a) The attractive forces between gas particles cause the true volume of the sample to be larger than predicted by the ideal gas law. (b) The attractive forces between gas particles most influence the volume of a sample at low pressure. (c) The volume of the gas particles themselves most influences the volume of the sample at low pressure. (d) The volume of the gas particles themselves causes the true volume of the sample to be larger than predicted by the ideal gas law.

Textbook Question

A glass tube has one end in a dish of mercury and the otherend closed by a stopcock. The distance from the surface ofthe mercury to the bottom of the stopcock is 850 mm. Theapparatus is at 25 °C, and the mercury level in the tube isthe same as that in the dish.

(a) Show on drawing (1) what the approximate level ofmercury in the tube will be when the temperature of theentire apparatus is lowered from +25 °C to -25 °C.