(b) Calculate the rms speed of NF 3 molecules at 25 °C.

Identify the formula for the root mean square (rms) speed: \( v_{\text{rms}} = \sqrt{\frac{3RT}{M}} \), where \( R \) is the ideal gas constant, \( T \) is the temperature in Kelvin, and \( M \) is the molar mass in kg/mol.. Convert the given temperature from Celsius to Kelvin by adding 273.15 to the Celsius temperature.. Determine the molar mass of NF 3 by adding the atomic masses of nitrogen (N) and fluorine (F) from the periodic table: \( M = M_N + 3 \times M_F \).. Convert the molar mass from grams per mole to kilograms per mole by dividing by 1000.. Substitute the values of \( R \), \( T \), and \( M \) into the rms speed formula and solve for \( v_{\text{rms}} \).

(b) Calculate the rms speed of NF 3 molecules at 25 °C.

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.10 - Gases

Problem 81b

Chapter 10, Problem 81b

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

Verified step by step guidance

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

Convert the given temperature from Celsius to Kelvin by adding 273.15 to the Celsius temperature.

Determine the molar mass of NF<sub>3</sub> by adding the atomic masses of nitrogen (N) and fluorine (F) from the periodic table: \( M = M_N + 3 \times M_F \).

Convert the molar mass from grams per mole to kilograms per mole by dividing by 1000.

Substitute the values of \( R \), \( T \), and \( M \) into the rms speed formula and solve for \( v_{\text{rms}} \).

Verified Solution

Video duration:

This video solution was recommended by our tutors as helpful for the problem above.

Was this helpful?

Key Concepts

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

Root Mean Square (RMS) Speed

The root mean square speed 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 energy and behavior of gas molecules.

Ideal Gas Law

The ideal gas law relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. This law assumes that gas molecules do not interact and occupy no volume, which simplifies calculations involving gas properties. Understanding this law is essential for deriving the RMS speed in the context of gas behavior.

Temperature Conversion

Temperature must be expressed in Kelvin for calculations in thermodynamics and gas laws. To convert Celsius to Kelvin, add 273.15 to the Celsius temperature. This conversion is necessary when calculating RMS speed, as the temperature directly influences the kinetic energy and speed of gas molecules.

Recommended video:

Guided course

02:10

Temperature Conversion Example

Previous problem

Next problem

Related Practice

Textbook Question

Suppose you have two 1-L flasks, one containing N2 at STP, the other containing CH4 at STP. How do these systems compare with respect to (a) number of molecules?

453

views

Textbook Question

Suppose you have two 1-L flasks, one containing N2 at STP, the other containing CH4 at STP. How do these systems compare with respect to (b) density?

395

views

Textbook Question

Suppose you have two 1-L flasks, one containing N2 at STP, the other containing CH4 at STP. How do these systems compare with respect to (c) average kinetic energy of the molecules?

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

Textbook Question

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

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

Verified Solution

Key Concepts

Root Mean Square (RMS) Speed

Ideal Gas Law

Temperature Conversion

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