(c) Calculate the most probable speed of an argon atom in the str...

Question

(c) Calculate the most probable speed of an argon atom in the stratosphere, where the temperature is 0 °C.

Accepted Answer

Welcome back everyone in this example, we're told that the temperature in the troposphere is 17°C. And what is the possible speed of a neon particle in the troposphere. So if we need to find the possible speed of this particle, that means we want to recall our formula for the speed of most probability. So that is what this represents, the speed. Or we can just say the most probable speed. And we should recall that this formula can be found or this value can be found by the following formula where we take the square root Of our gas constant r. times our temperature in Kelvin. This is multiplied by two and then divided by the molar mass of our gas particle. So we want to recall that our temperature should be in units of Kelvin, meaning that will take the 17°C from the prompt and add to 73.15. To get our Kelvin temperature equal to 2 90.15 Kelvin. So now that we've recalled the above, we're going to get into our formula to find the most probable speed of our neon particle. And we would say that that is equal to our square root of two, multiplied by r. Gas constant R. Which we recall is a value of 8.314 with units of kilograms times meters squared divided by second squared times moles times kelvin. So this is our constant r. And then we want to continue this underneath our square roots and where we have our temperature that we converted as to 90.15 Kelvin. And then in our denominator, we have our molar mass of our neon particle. So looking at our periodic table, we would see that we have a molar mass of neon equal to 20.18 g per mole. So we'll plug that in as 20.18 g per mole. But as you see in our units for our gas constant R. We need to get rid of our kilogram unit. And so we're going to actually convert this molar mass two units of kilograms. So we're gonna recall that our prefix kilo tells us that we have for one kg our base unit 10 to the third power grams. And this allows us to cancel out grams and leave us with kilograms. However, we can now cancel out kilograms with kilograms in the numerator. We can cancel it, cancel out kelvin with kelvin here in r gas constant R. And we can also get rid of our unit with moles with moles in the denominator. And because we have everything under our square root symbol that leaves us with one unit of meters and one unit of our seconds. And so in our calculators, we're going to get a value for our most probable speed of our neon particle equal to 489 m per second. And so for our final answer, that is what we have here highlighted in yellow as are possible speed of our neon particle. So I hope that everything I explained was clear. If you have any questions, please leave them down below, and I will see everyone in the next practice video.

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