A 113-mL gas sample has a mass of 0.171 g at a pressure of 721 mmHg and a temperature of 32 °C. What is 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 equation. So, first I want to go ahead and sort out my information from what were given in the problem. So, given information We can see here that were given a pressure of 8:13 M M H G. And were given a temperature of 41°C. We also have a volume of 207 ml of the gas sample and we have a mass of 6.52 g where we're trying to solve this problem here, it says we're trying to calculate the molar mass. Alright, so first we know that we have given a pressure given a temperature and we're given a volume and the P the ideal gas law equation is the PV equals N. R T R is going to be ideal gas law constant. This can be found in textbooks are given to you by professor, but it is a constant. That our value is going to be equal to 0.08206. The units of A T. M. Times leader all over, kelvin times. All right, let's see here. I have stated that we have given the P and the V. Were given are are like here and we're given our temperature. What we want to find is our end because that's what we are going to be putting into the molar mass calculation. So I want to go ahead and manipulate my equation first. Since we're solving for the end, I'll divide each side by R. T. You can see here now that those two cancel isolating just our end. So N. Is equal to P. V over R. T. Alright. So whenever doing ideal gas law equation problems, we see that we have this constant here with a bunch of different units, any data values that we're going to plug into this equation here. We want the units to also match with the constant because this will never change. So let's see where we want our pressure to be an ATM. So we have the mm H. G. We want the temperature to be in kelvin's but we see here we have Celsius and we want the volume in liters milliliters. So we have a little bit of convergence to do before I can plug in values. So first let's start off with the pressure. So given 8 13 M. M H. G. And covering that into A T. M. My denominator will be 7 60. Mm H G. All over 1 80 M. You can see now that the mm hg will cancel and will leave a final answer with a T. M. As the units. So that's going to equal to 1.06 80. And next will be my temperature. So we're given the 41°C how we convert that to Kelvin is just by adding 2 73 0.15. So putting that into my calculator, I'll get 3 14.15 kelvin's Alright. And lastly we're going to be doing the volume point version into leaders. So we're given the 207 ml. We will convert that into L. So every leader has 1000 ml. All right. Going ahead to cancel the email internet. You can see here that the final answer will be in leaders And putting that into my calculator. I'll get 0.207 L as my volume. Alright now we can go ahead and finally plugging all the values in our equation. So, and it's going to be eagling to our pressure Which we have sulfur which is 1.0697 A T. M. Multiplied by the volume Which is 0. L. That's going to be divided by Our gas law constant which is 0.08206 units being 80m times later. All over Kelvin time small and of course multiplied by our temperature Which is 14.15 Kelvin's. And you can see here the A T. M will cancel. Leader will cancel and Calvin's will cancel Putting everything into my calculator. I will get my end value to be 0. 589 moles. And again we are solving for a molar mass. So moller mass. The unit is going to be grams per moles. We can see that we have this mole here and we have our grams here that's given to us. So let's go ahead and solve our molar mass. So more mass is equal to the grams on top, So 6.52 g. And of course the moles is what we just saw for right over here. That's going to be 0. 85 89 moles. Putting everything into my calculator by numerical value is going to be 759 and then units do not cancel out. But that's what we want because molar masses in g per month. So that is going to be my final answer for this problem. Thank you everyone for watching.

A 113-mL gas sample has a mass of 0.171 g at a pressure of 721 mmHg and a temperature of 32 °C. What is the molar mass of the gas?

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Key Concepts

Ideal Gas Law

Molar Mass

Gas Properties and Units