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

검증된 단계별 안내

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).

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

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.

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.

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.

관련 실천

교과서 질문

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

교과서 질문

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

교과서 질문

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