At 25 °C (approximately room temperature) the rms velocity of an Ar atom in air is 1553 km/h. (c) What is the total kinetic energy of 1 mol of Ar atoms moving at this speed?

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Welcome back everyone in this example, we need to calculate the kinetic energy of an oxygen molecule at 30 degrees Celsius. So the key word here is molecule for our oxygen species. And we're going to recall our kinetic energy formula for one mole of a gas is going to be equal to three halves, multiplied by the moles of our gas times r gas constant R and then times our temperature in kelvin. Where again, n would be the moles of our gas molecule. Now we're going to interpret this in terms of molecules of our gas. So in this case we would say that kinetic energy of our oxygen should be equal to three halves times R gas constant, R times r temperature in kelvin divided by avocados number. So that's representatives N. A. So we would recall that avocados number tells us that we have 6.022 times 10 to the 23rd power molecules. And sorry, that's molecules per mole of our gas. And we should recall that according to kinetic theory, molecules will undergo elastic collisions, just like gasses are stated to in our kinetic theory. And so that is according to our kinetic theory for ideal gasses. So now that we have our formula laid out, we're gonna plug in what we know but we also want to make sure we convert our temperature to kelvin. So we're gonna add to 73.152 R 30 degrees Celsius. And that's going to give us our kelvin temperature equal 2 to 73.15 kelvin. So now let's go go ahead and plug everything in. So we would say that our kinetic energy of our oxygen molecule is equal to three halves multiplied by r gas constant. R which we should recall is equal to a value of 8.314 with units of jewels divided by moles times kelvin. This is then multiplied by our temperature in kelvin which we converted 2 to 73. kelvin. And then in our denominator we have our avocados constant which we understand is equal to six point oh 22 times 10 to the 23rd power. And this unit of molecules which we want to divide by moles because we want moles to cancel out with moles in our numerator. So we'll get rid of moles here as well as here will also be able to cancel out our units of kelvin and we're left with units of joules per molecule as our final units. And so for our final answer, we understand the kinetic energy of an oxygen molecule is going to equal a value of 6.278 times 10 to the 21st power jewels per molecule. And so what's highlighted in yellow here is our final answer to complete this example, I hope that everything I reviewed was clear if you have any questions, leave them down below and I'll see everyone in the next practice video

At 25 °C (approximately room temperature) the rms velocity of an Ar atom in air is 1553 km/h. (c) What is the total kinetic energy of 1 mol of Ar atoms moving at this speed?

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Key Concepts

Root Mean Square Velocity (rms velocity)

Kinetic Energy of Gas Particles

Molar Mass