The molar mass of a volatile substance was determined by the Dumas-bulb method described in Exercise 10.53. The unknown vapor had a mass of 2.55 g; the volume of the bulb was 500 mL, pressure 101.33 kPa, and temperature 37 °C.Calculate the molar mass of the unknown vapor.

Video transcript

hi everyone for this problem, we are being asked to calculate the molar mass of the unknown liquid. Using the given information obtained via the Duma's method were given the mass of the vapor volume of flask, pressure and temperature. So let's go ahead and get started. The do miss method. The dooms vapor density equation is pressure times volume is equal to mass times. Are gas constant times temperature over moller mass. And for this question we're solving for moller mass. So we need to rearrange this equation to reflect that when we rearrange the equation we get R molar mass is going to equal M R T over P V. Okay, so let's go ahead and plug in what we know based off of what we're given. I'll move this over here so we can have some space. So we know that our mass of the vapor is 1.3 to 14 g. Okay, so let's go ahead and plug that in 1.3214g. Okay, so we have the mass R R gas constant. It's not given but it is something that we should know. R is equal to 0. Leaders times atmosphere over mole times kelvin. So we can plug that in. Okay, our temperature, they tell us our temperature is 99.43 degrees Celsius. But if you look at our gas constant. R R unit for temperature is kelvin. So that means we need to convert this from degrees Celsius to kelvin. And the way that we do that is by adding 273.15. When we do that we get a temperature of 372.58 Kelvin. Okay so we can go ahead and plug that in. So that's our numerator And this is all over pressure times volume. We're told that our pressure is 754.3. Tour. If we look at our gas constant R. Pressure is an A. T. M. So we need to convert this. So 754.3 tour to A. T. M. We need the unit conversion and 1 80 M. There. 760 tour. So our tourists cancel here and we're left with A. T. M. And when we solve that out we get 0. A. T. M. Okay, so we can go ahead and plug that in and our volume, they gave it to us in milliliters and we need to convert this to Leaders because our gas constant is in leaders. So we need to divide by 10 to the -3. Okay, so that gives us a volume of 0.500 L. So let's go ahead and plug that in 0.500 L. Okay, so now we have everything that we need to solve this out. So let's go ahead and write out that conversion for Um ml two leaders just so that you can have it. So we're told that we have 500 mL in one leader And one middle leader. We have 10 to the negative three leaders. Okay, So that gives us that 0.500 l because our milliliters cancel. All right. So we get a final answer of 81.41 grams per mole. This is going to be our molar mass using the Duma's method. That's the end of this problem. I hope this was helpful.