Calculate the root mean square velocity of F 2 , Cl 2 , and Br 2 at 298 K.

Hey everyone. So here we asked. The root mean square velocities of chlorine gas, argon gas, hydro biotic acid. And the temperature is 300 Kelvin. So the root mean square velocity Visit to the Square Root of three R. T. About about a Mueller mass. So far our value have 8. jaws about about moles tom's kelvin. And we know that jules executive kilograms, thomas meter squared about by seconds squared. So far our value of 8. kilograms times meters squared. About about malls times kelvin times seconds squared. Look at the root mean square velocity of chlorine gas, We're gonna get three Times 8. telegrams. I'm his meter squared, invited by malls times Calvin second squared Times 300 Kelvin by the molar mass. It's gonna be too It was a massive chlorine which is .453. This give us 70 .906g. But this has to be in kilograms. They're gonna have 70 .906g In 1000 g of one kg And it will give us 0.0709 telegrams 0.0709 kilograms per mole solar mass. This give us 324 0.87 Minutes for a 2nd. The root mean square velocity of argon gas. We're gonna have the square root three 8.314 milligrams. House meter squared. What about mose name's Calvin? I'm second squared Times 300 Kelvin by the molar mass. And this is 39.948. We need to convert two kg 1000 g in one kg. And this will give us 0.39 telegrams, 0.39 948 kilograms per mole. The molar mass This gave us 0.79. Meet us for a second at the root mean squared velocity of hydro biotic acid. It's going to be the square root three Times 8.314 kilograms times meters squared. What about moles, thomas, kelvin, second squared Times 300 Kelvin by by the molar mass hydro biotic acid. It's gonna be a mass of hydrogen which is 1.008 g. That's a massive iodine. 126 .904. Nice to give us 127 .912 grams. We need to convert two kg 1000 g of one kg. This will give us 0.12 telegrams, 0.12 7912 kilograms per mold the molar mass. And this will give us 241 0.86. Meet us for a second. Thanks for watching my video and I hope it was helpful

Ch.5 - Gases

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Tro 4th Edition

Ch.5 - Gases

Problem 83a

Chapter 5, Problem 83a

Calculate the root mean square velocity of F₂, Cl₂, and Br₂ at 298 K.

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Identify the formula for root mean square velocity: $v_{rms} = \sqrt{\frac{3RT}{M}}$, where $R$ is the ideal gas constant, $T$ 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. For example, F$_2$ has a molar mass of approximately 38 g/mol, which is 0.038 kg/mol.

Use the ideal gas constant $R = 8.314 \text{ J/(mol K)}$ and the given temperature $T = 298 \text{ K}$ in the formula.

Substitute the values for $R$, $T$, and the molar mass $M$ for each gas into the root mean square velocity formula.

Calculate the root mean square velocity for each gas using the substituted values.

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Key Concepts

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

Root Mean Square Velocity (rms velocity)

Root mean square 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 in kg/mol. This concept is crucial for understanding the kinetic theory of gases, which relates temperature to molecular motion.

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). For diatomic molecules like F2, Cl2, and Br2, the molar mass is calculated by summing the atomic masses of the constituent atoms. Knowing the molar mass is essential for calculating the rms velocity, as it directly influences the speed of gas particles at a given temperature.

Kinetic Theory of Gases

The kinetic theory of gases describes the behavior of gases in terms of particles in constant motion. It explains how temperature, pressure, and volume relate to the motion and energy of gas molecules. This theory underpins the derivation of the rms velocity formula and helps predict how different gases will behave under similar conditions, such as temperature.

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Calculate the root mean square velocity of F2, Cl2, and Br2 at 298 K.

Verified video answer for a similar problem:

Key Concepts

Root Mean Square Velocity (rms velocity)

Molar Mass

Kinetic Theory of Gases

Calculate the root mean square velocity of F₂, Cl₂, and Br₂ at 298 K.