The root mean square speed of gas molecules is 283.0 m/s at a given temperature T when the recorded molar mass is 42.0 g/mol. What would be the root mean square speed for a gas with a molar mass of 152.0 g/mol?

Here in this practice question it says, the root mean square speed of gas molecules is 283 meters per second at a given temperature t when the recorded molar mass is 42 grams per mole. What would be the root mean square speed for gas with a molar mass of 152 grams per mole. Alright. So we're being given quite a bit of information, but let's focus on the first sentence. They're talking about root mean square speed, so that equals square root of 3 r t over molar mass. Let's plug in the information given to us. We have 283 meters per second, and that's gonna equal square root of 3 times our r constant of 8.314. We'll forego units for now because we know what units there should be. Temperature, we're looking for it. Molar mass, remember, is in kilograms per mole, not grams per mole. So we have to convert this 42 grams per mole to 0.042, worth now kilograms per mole. We got to get rid of this square root, so we square both sides. When we do that we're gonna have 8 0089 equals, multiplying 3 times 8.314 gives us 24 0.942, still times t, divided by 0.042. Multiply both sides by 0.042, and that's gonna give us here, let's see, 3363.738 equals 24 24.942 still times t. Divide out 24.942, and when we do that we'll find our temperature. So when we do that we get our temperature equal to 134.86 Kelvin. We did all that work so that we could find temperature. Now that we know temperature, we can look at the second sentence. So now they're telling us we have a new molar mass of 152 grams per mole, and that'll help us figure out our new root mean square speed. So that equals 3 times 8.314 times our 134.86 divided by the new molar mass, which is 0.152 kilograms per mole. Plugging that in gives us our final answer of 148.8 meters per second for our root mean square speed. So that's the answer we get at the end when we do this following, substitution of temperature into our new root mean square speed form.

The root mean square speed of gas molecules is 283.0 m/s at a giv...

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The root mean square speed of gas molecules is 283.0 m/s at a given temperature T when the recorded molar mass is 42.0 g/mol. What would be the root mean square speed for a gas with a molar mass of 152.0 g/mol?

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Root Mean Square Speed practice set