Skip to main content
Ch.10 - Gases
Brown - Chemistry: The Central Science 14th Edition
Brown14th EditionChemistry: The Central ScienceISBN: 9780134414232Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoBrown 14th EditionCh.10 - GasesProblema 82c2
Capitolo 10, Problema 82c2

(c) Calculate the most probable speeds of Cl2 molecules at 300 K.

Guida verificata passo dopo passo
1
Identify the formula for the most probable speed of a gas molecule, which is given by \( v_p = \sqrt{\frac{2kT}{m}} \), where \( v_p \) is the most probable speed, \( k \) is the Boltzmann constant, \( T \) is the temperature in Kelvin, and \( m \) is the mass of a single molecule.
Convert the molar mass of \( \text{Cl}_2 \) from grams per mole to kilograms per molecule. The molar mass of \( \text{Cl}_2 \) is approximately 70.9 g/mol. Use Avogadro's number \( 6.022 \times 10^{23} \) to find the mass of one molecule.
Substitute the values into the formula: \( k = 1.38 \times 10^{-23} \text{ J/K} \), \( T = 300 \text{ K} \), and the calculated mass of a \( \text{Cl}_2 \) molecule.
Calculate the expression under the square root to find the most probable speed.
Ensure the units are consistent throughout the calculation to obtain the speed in meters per second (m/s).

Risposta video verificata per un problema simile:

Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.
Durata del video:
3m

Concetti chiave

Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.

Kinetic Molecular Theory

Kinetic Molecular Theory explains the behavior of gases in terms of particles in constant motion. It posits that the temperature of a gas is directly related to the average kinetic energy of its molecules. This theory helps in understanding how temperature influences the speed of gas molecules, which is crucial for calculating the most probable speed.
Video consigliato:
Percorso guidato
01:19
Kinetic Molecular Theory

Most Probable Speed

The most probable speed of gas molecules is the speed at which the largest number of molecules are moving at a given temperature. It can be calculated using the formula v_mp = sqrt(2kT/m), where v_mp is the most probable speed, k is the Boltzmann constant, T is the temperature in Kelvin, and m is the mass of a molecule. This concept is essential for determining the speed of Cl2 molecules at 300 K.
Video consigliato:
Percorso guidato
01:35
Most Probable Speed Example

Molar Mass and Gas Constant

Molar mass is the mass of one mole of a substance, which is critical for converting between grams and moles in calculations. For Cl2, the molar mass is approximately 70.9 g/mol. The gas constant (R) is used in various gas equations and relates to the behavior of gases under different conditions, aiding in the calculation of molecular speeds.
Video consigliato:
Percorso guidato
00:51
The Ideal Gas Law: Molar Mass
Pratica correlata
Domanda del libro di testo

Which one or more of the following statements are true? (a) O2 will effuse faster than Cl2. (b) Effusion and diffusion are different names for the same process. (c) Perfume molecules travel to your nose by the process of effusion. (d) The higher the density of a gas, the shorter the mean free path.

1028
views
Domanda del libro di testo

At constant pressure, the mean free path 1l2 of a gas molecule is directly proportional to temperature. At constant temperature, l is inversely proportional to pressure. If you compare two different gas molecules at the same temperature and pressure, l is inversely proportional to the square of the diameter of the gas molecules. Put these facts together to create a formula for the mean free path of a gas molecule with a proportionality constant (call it Rmfp, like the ideal-gas constant) and define units for Rmfp.

951
views
Domanda del libro di testo

(b) Calculate the rms speed of NF3 molecules at 25 °C.

1243
views
Domanda del libro di testo

(c) Calculate the most probable speed of an ozone molecule in the stratosphere, where the temperature is 270 K.

521
views
Domanda del libro di testo

(c) Calculate the most probable speeds of CO molecules at 300 K.

123
views