 Let's solve a couple of questions on RMS speed and average kinetic energy of gas molecules. First question says, at what temperature is the RMS speed of nitrogen the same as that of Oxygen's RMS speed at 2 degrees Celsius? And we are given the molecular masses of Oxygen and Nitrogen. Report your answer to two significant figures, and we need to report it in degree Celsius. Okay, as always pause the video, first try this one on your own. Alright, hopefully you have given this a short. Now the RMS speed of any gas molecule that is V RMS, this is given by, this is given by this relation 3RT divided by M, R is the gas constant, T is the temperature, M is the molecular mass of that gas. And in the question we are given that the RMS speed of Nitrogen, so let's write V RMS N2, this is equal to, this is equal to the RMS speed of Oxygen, the RMS speed of Oxygen at 2 degrees Celsius. So what we can do is, we can equate this equation for both of them, so on the left hand side we can write 3RT divided by the molecular mass of Nitrogen, this is equal to 3R into T. Now T for Oxygen, we know that we need to take temperature of 2 degrees Celsius, but here we write it in Kelvin's and reporting everything in Kelvin's means adding 273 to it, so you add 273 to the degree Celsius and that is, that is your Kelvin. So here it will be 273 plus 2 degrees Celsius, so Kelvin this will be 275 divided by the molecular mass of Oxygen, this is MO2. Now we can move the square roots of both sides and we can also cancel off 3R, we can cancel off 3R. So what remains is T, T divided by molecular mass of Nitrogen that is 28, this is equal to 275 divided by molecular mass of Oxygen that is 32 and when we work this out, when we work this out, I encourage you to pause the video and work out this calculation. When you do work it out, you should get T in Kelvin as 240.625 Kelvin's, when we change this to degree Celsius, we would need to subtract 273 from this, so Celsius writing this in Celsius really means K minus 273 that is degree Celsius and this is in Kelvin, so 240.625 minus 273 and when you do that, when you do that 240.625 minus 273, this comes out to be equal to minus 32.375 degrees Celsius. We need to report the answer to two significant figures, so we can do that and we can write this as minus 32 degrees Celsius, so this is minus 32. Okay let's look at one more question. Here Oxygen and Hydrogen are kept at the same temperature, choose the correct statements about the RMS speeds of the gases and the kinetic energies of its molecules. We need to choose two answers out of these, how many, these six options. So let's look at each option one by one and see whether it's correct or not. So for the first one, VRMS, VRMS of Oxygen is more than VRMS of Hydrogen. Let's think back to what was RMS speed. RMS speed was proportional to, it is really proportional to temperature divided by the molecular mass of that gas and when you remove the proportionality, you add a constant of 3R, but it's proportional to T by M, the square root of T by M, so if both of them are kept at the same temperature, T is same for Oxygen and Hydrogen, but the molecular mass of Oxygen is way more than the molecular mass of Hydrogen, which means if molecular mass is more, if this is more, VRMS for that gas should be less, but over here it's written that VRMS of Oxygen is more than VRMS of Hydrogen, so this one is wrong, this one doesn't make sense, because molecular mass of Oxygen is more than that of Hydrogen, so if the denominator is more, if the denominator is more, the RMS speed for that should really be less and the second one by the same line of reasoning is right. So for, for Hydrogen, for Hydrogen, the molecular mass is much less than Oxygen, which means that the RMS speed of Hydrogen, RMS speed of Hydrogen must be more than that of, than that of Oxygen, so this one is correct. Now the third one says they are equal, this is again wrong, because we just talked about how the second option is right. Now they are talking about kinetic energy, so let's think back to what was kinetic energy, the average kinetic energy of gas molecules. Average Ke, that was Ke average, this was really, this was really equal to 3 by 2 into Boltzmann constant, K multiplied, K multiplied by temperature. Now kinetic energy only depends on temperature, so if these two gases are kept at the same temperature, the average kinetic energy of the gas molecules must be the same for both of them. So both D and E are wrong, in fact the right answer is option F, because it only depends on temperature and they are kept at the same temperature, so the kinetic energy for Oxygen and Hydrogen must be the same. You can try more questions from this exercise in this lesson and if you're watching on YouTube, do check out the exercise link which is added in the description.