A sample of gas has a mass of 38.8 mg. Its volume is 224 mL at a temperature of 55 °C and a pressure of 886 torr. Find the molar mass of the gas.

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Hello everyone in this video. We're going to be dealing with the ideal gas law. So first I want to go ahead and sort out my data from what we have by reading the problem. So first Oh, I know what we're given and that is going to be let's see. We have a temperature given to us as 68 degrees Celsius. We also have a pressure of 893 tour, we have a volume of 12. ml And we have a mass of mg. And what the problem states that we're trying to find our solved for is the molar mass of a guess. All right. And of course the molar mass units as we know is grams per mole. All right. So the ideal gas law equation is P V equals N R T. And we can see from this problem we are given our T were given the pressure. Soapy and were given the volume. Sorry, this is the volume. Alright, so we have our p value, we have RV we have R T R is something that Is textbook which is going to be equaling to the 0.08206 units of ATM times later over kelvin's time small since this is a constant, this will never change as well as the units, the units will never change. And because we have this constant here, any values that we're going to plug in to our equation here. We want the units to match our constant, not the other way around. So for starting off with our temperature here, we know we want kelvin's but this is in Celsius. So we do some conversions and for pressure we want a TM tour, we want to go ahead and also do some calculations as for volume, we want that to be in leaders and this is in milliliters. So again we need to do those conversions. So let's first start off by doing those conversions before anything else. So starting off with my temperature, We have the 68°C. How we convert that into Kelvin's is by adding 273 0.15 kelvin's in putting that into my calculators will get the conversion into 341.15 Kelvin's Next will be my volume. So 12.4 ml And two leaders. So every 1000 millions is one leader. As you can see Miller's Balkans out leaving us with 0.0124 and leaders as our units. Lastly we have our pressure. So we're given 893 tour how we convert that into ATM. Is that every A. T. M. We have 760 Tour again, you can see that our tour unit will cancel it out And our answer putting that into my calculator, I get 1.175 A. T. M. And because we're solving for end, I'm going to go ahead and manipulate my equation here a little bit divide each side by R. T. So that I can get And by itself. So dragging that down here, we can see that end. We're equal to P. V. Over R. T. Now actually playing in values. So pressure we calculated was 1.7 or 1.175 A. T. M. And our volume is 0.0124 leaders. That's going to be divided. Oliver bar constant which is 0.8206 units being A. T. M. Times leaders over kelvin times Our temperature is 3 41.15 Kelvin. As you can see our units of A. T. M. Will cancel. Leaders will cancel and kelvin will cancel and plugging that into my calculator. I'll get a morph of 0. 052045 malls. All right. So first things first we have to realize that the molar mass. We need grams per mole here. Which sulfur our mole here. We need to convert the milligrams into grounds. So We have 1 mg. And covering that into just g. We have 1000 mg per one g. The units of milligrams will cancel, Leaving us with 0.178 grounds. No. Finally finding our molar mass. So we want grams on top or treat a software of 0.178 g. And then the movie which we saw for right here is 0. 52045 malls. So plugging that into my calculator. My final value for my molar mass is Graham's Permal, and that would be my final answer for this problem.

A sample of gas has a mass of 38.8 mg. Its volume is 224 mL at a temperature of 55 °C and a pressure of 886 torr. Find the molar mass of the gas.

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Key Concepts

Ideal Gas Law

Molar Mass

Unit Conversion