Which has a higher average speed, H2 at 150 K or He at 375 °C?

Video transcript

Welcome back everyone. We need to identify the gas that would have a lower mean speed. Either krypton at 15 degrees Celsius or chlorine gas at 300 degrees kelvin. So we're going to have to calculate the mean square speed for both of these gasses. We're going to begin by recalling our formula for root mean square speed represented by this symbol, which is set equal to the square root of three, multiplied by r gas constant. R multiplied by r temperature in kelvin, which is then divided by our molar mass of our gas in units of kilograms per mole. So we're going to begin by calculating the molar mass of first krypton gas, which, from our periodic table we can see is equal to 83.8 g per mole because it's in Group 88 in the noble gas group. And we're going to convert this to two kg by multiplying by kilograms and grams in the denominator where one g we would recognize as equivalent to 10 to the negative third power kilograms, canceling out our units of grams were left with kilograms per mole as our final unit. And this is going to give us a molar mass equal to 0. kg per mole for our krypton gas. So now we can next go into calculating the temperature which should be in kelvin where were given 15 degrees Celsius, we're going to add to 73.15. And that's going to give us our kelvin temperature equal to 288. kelvin. So now calculating the root, mean square speed of our krypton grass gas, this is set equal to the square root of three times r gas constant. R 8.314 joules divided by moles, times kelvin multiplied by our temperature. We just calculated the temperature as 288.15 Kelvin. So now we're going to and let's fix that. We're going to divide by our molar mass for Krypton which we just converted to kg per mole as 0.083, eight kg per mole. So simplifying this, we want to recall that we have a conversion factor where one jewel is equivalent to one kg times meter squared divided by seconds squared. So we're going to interpret our jewel units as follows in the second line and what we'll have is 6987.5 under a square root with units of kilograms times meters square divided by seconds squared divided by moles times kelvin multiplied and sorry, not multiplied by anything because we took the product of these two values. Three values here. This is now going to leave us with our denominator of 0.0838 kg per mole. So now canceling out our units, we will have been able to get rid of Kelvin. So we actually did not need to write that there, we can cancel out our mole units as well as our kilogram units. And when we take the square root in our next step, we're going to be left with one unit of meters and one unit of seconds. So kelvin was actually canceled out in the first step when we took the products. And what we'll be able to say is that our main square speed of krypton is now equal to. And sorry, just to make a correction here. When we took the product of these three numbers, we should have yielded a result of 7187. and interpreting our units as kilograms times meters squared divided by seconds squared, divided by moles after we canceled out kelvin. So now this is going to yield a main square speed for krypton equal to 293 m/s. So now moving on to our next gas, which is our chlorine gas, we're going to begin by calculating the molar mass of chlorine gas from our periodic table, where we would find chlorine in group seven a corresponding to a molar mass of 70.9 grams per mole. Since we have two atoms of chlorine, which we will now convert to kilograms by multiplying by 10 to the negative third power kilograms equivalent to one g, canceling out units of grams. This gives us a molar mass for chlorine gas equal to 0.709 kg per mole. So now calculating our root mean square speed of chlorine gas at 300 Kelvin, we're gonna go into our formula so that we have the square root of three multiplied by r gas constant. R 8.314 jules divided by moles. Times kelvin multiplied by our temperature. In kelvin. Given us 300 kelvin from the prompt, divided by our molar mass, which we just found to be 0.709 kg per mole. So simplifying this, we're going to have in our next line, the square root of our products of the first three terms in the numerator equal to 7482.6. And now we're going to interpret our units of jewels as kilograms times meters squared divided by seconds squared, divided by moles. Because kelvin would have canceled that when we took the product in our first step. And this is all divided by our denominator. And let's make this clear. This is all divided by our denominator of 0. kg per mole. So now canceling out our units, we can get rid of kilograms, we can get rid of moles and we can get rid of one of our meters and one of our seconds, leaving us with one m and one second. And now we're going to have for our final answer for the mean square speed of chlorine gas at 300 Kelvin being equal to a value of 320 4.8, which we can round to about 325 m per second. And so now going back to our prompt, we need to figure out which of these mean square speeds between these gasses is lower. So we're going to compare and say that Or rather 293 meters per second as our mean square speed of our krypton gas is less than our mean square speed of our chlorine gas, which we just found to be 325 m per second. And so for our final answer, we would say that we would say therefore krypton at 15°C according to the prompt, has a lower mean square speed and this would be our final answer. To complete this example. I hope everything that I reviewed was clear. If you have any questions, please leave them down below and I will see everyone in the next practice video.