A sample of N2O gas has a density of 2.85 g/L at 298 K. What is the pressure of the gas (in mmHg)?

Video transcript

Hey everyone in this example, we're working with nitrogen dioxide gas with a density of 3.27 g per liter at 315 kelvin and we need to figure out the pressure of this gas in millimeters of mercury. So we're going to recall our formula for the density version of our ideal gas law. And that models after this formula where we have pressure equal to the substitution for density, which is going to be mass divided by volume. And then we're going to multiply this quantity by r gas constant R times temperature in kelvin divided by the molar mass of our given gas. And so again, we want to go ahead and make sure that our temperatures in Kelvin. So it is given to us in Kelvin. We are also given our quantity for density here 3.27 g/l. And we should recall that our gas constant R is 0.8 to one Leaders times a t m's divided by moles, times kelvin. So we can go ahead and plug in all of our known given info. So what we should have is pressure is equal to our given density 3.27 g per liter. We're multiplying this density quantity by our gas constant R 0.08-1 Leaders times ATMs divided by moles times kelvin. And then next we're going to multiply by our temperature in Kelvin given as 315 Kelvin. And dividing that by our molar mass of nitrogen dioxide, which when we refer to our periodic tables, the molar mass of nitrogen dioxide is equal to 44.013 g per mole. So we can go ahead and plug this quantity in And sorry, that should be 44. And when we do so, we can go ahead and before we calculate this in our calculators, let's go ahead and cancel our units. So we can cancel out our kelvin's. We can also cancel out moles. Next we can get rid of gramps, we can get rid of leaders. And that leaves us with our only unit. We haven't canceled which is A. T. M's. So now we can go ahead and calculate the quantity for pressure in our calculators and we should get a value equal to 1.9 to 1 ATMs. Now again, this question is asking us to give our pressure in millimeters of mercury. And so we want to recall the conversion factor where we have one A. T. M. Equalling 760 of Mercury. And so we can go ahead and use this conversion factor. So in our numerator we're going to have 760 millimeters of mercury and inner denominator, we have one ATM. So we're going to go ahead and cancel out ATMs with one another. We're left with our final unit millimeters of mercury. And when we get our final quantity for pressure we should get a value equal to 1,460. mm of mercury. And so this will complete this example as our final answer for our pressure of our nitrogen dioxide gas in mm of mercury. So I hope that everything we reviewed was clear. If you have any questions, please leave them down below, and I will see everyone in the next practice video.