 The lethal dose of hydrogen cyanide gas which has the formula HCN for an adult is about 120 milligrams. First of all I want to know what's the volume at STP of 120 milligrams of HCN and then we'll work out how many molecules of HCN are in this volume. So let's take this first problem first. We're going from a mass to a volume. So that's our strategy. The conversion factors we're going to need are the molar mass of hydrogen cyanide and the molar volume of the gas at STP which we know is 22.4 litres per mole. Now there's one other thing. This mass is expressed in milligrams not in grams. So we're going to have to include a unit conversion to get that mass into grams so that the units will cancel out nicely with the molar mass which is in grams per mole. So let's work this through step by step. First we write down what we know, 120 milligrams of HCN and then we're going to convert this into grams. So we want the conversion factor for milligrams to grams and we know that there are 1000 milligrams in one gram. So I'm going to put the milligrams on the bottom so that they cancel and the grams on the top. Alright so if I were to calculate this out now it would give me this mass in grams. But I'm going to keep going so that I can make it one single calculation at the end which is slightly more efficient. Okay I have changed my mass from milligrams to grams. The next step is to change the mass in grams to moles. So I need the molar mass as a conversion. I haven't calculated the molar mass yet so I'm going to need to go back and do that. And I'm going to need the molar masses of hydrogen, carbon and nitrogen which gives me the molar mass of 27.026 grams per mole. Okay there's my conversion factor. Now I need to put it into my calculation. I have grams on the top. I want to cancel out the grams. So the conversion factor is going to be written with its grams on the bottom and moles on the top. Alright I've now converted my mass into moles. The last step of my conversion is to convert the moles into volume using the molar volume as a conversion factor. I have moles but I want to go to liters so I want the moles to cancel. So I'm going to write the conversion factor with the liters part on the top and the moles part on the bottom. Moles cancel and I'm left with liters. Now I run through the calculation. And when I plug that into the calculator I don't forget to put the bottom in brackets so that the order of operations is preserved. And that gives me the answer of 0.09946 liters. I go back to check my sig figs. The original mass that I was given has only two sig figs so I need to round this off. Becomes 0.099 liters which is about 100 mls of gas which really isn't very much.