Calculate the root mean square velocity and kinetic energy of F₂, Cl₂, and Br₂ at 298 K. Rank these three halogens with respect to their rate of effusion.

검증된 단계별 안내

Identify the formula for root mean square velocity: \(v_{rms} = \sqrt{\frac{3RT}{M}}\), where \(R\) is the ideal gas constant (8.314 J/mol·K), \(T\) is the temperature in Kelvin, and \(M\) is the molar mass in kg/mol.

Convert the molar masses of F\(_2\), Cl\(_2\), and Br\(_2\) from g/mol to kg/mol. F\(_2\) = 38.00 g/mol, Cl\(_2\) = 70.90 g/mol, Br\(_2\) = 159.80 g/mol.

Substitute the values of \(R\), \(T\), and \(M\) for each gas into the root mean square velocity formula to calculate \(v_{rms}\) for F\(_2\), Cl\(_2\), and Br\(_2\).

Use the kinetic energy formula \(KE = \frac{1}{2}mv^2\) to calculate the kinetic energy for each gas, where \(m\) is the molar mass in kg/mol and \(v\) is the root mean square velocity.

Apply Graham's law of effusion, which states that the rate of effusion is inversely proportional to the square root of the molar mass, to rank F\(_2\), Cl\(_2\), and Br\(_2\) in terms of their rate of effusion.

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.

Root Mean Square Velocity

The root mean square (RMS) velocity is a measure of the average 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 temperature in Kelvin, and M is the molar mass of the gas. This concept is crucial for understanding how the speed of gas molecules relates to their mass and temperature.

Kinetic Energy of Gases

The kinetic energy of gas molecules is directly related to their temperature and can be expressed using the formula KE = (1/2)mv^2, where m is the mass and v is the velocity of the gas particles. At a constant temperature, the average kinetic energy of gas molecules is the same, which allows for comparisons between different gases based on their molar masses.

Graham's Law of Effusion

Graham's Law states that the rate of effusion of a gas is inversely proportional to the square root of its molar mass. This means lighter gases effuse faster than heavier gases. Understanding this law is essential for ranking the rates of effusion of F2, Cl2, and Br2, as it allows us to predict which gas will effuse more quickly based on their respective molar masses.

Calculate the root mean square velocity and kinetic energy of F2, Cl2, and Br2 at 298 K. Rank these three halogens with respect to their rate of effusion.