Hydrogen cyanide, HCN, is a poisonous gas. The lethal dose is approximately 300 mg HCN per kilogram of air when inhaled. (a) Calculate the amount of HCN that gives the lethal dose in a small laboratory room measuring 3.5 * 4.5 * 2.5 m. The density of air at 26 C is 0.00118 g>cm3.

Video transcript

we have a question telling us that a concentration of 100 mg of hydrogen sulfide park kilogram of air can already cause various respiratory symptoms. What is the mass of hydrogen sulfide present in a 4.0 times 5.5 times 3.5 centimeter room that is contaminated with that concentration of hydrogen sulfide. Assume that the density of air is 0.1225 g per centimeters cubed. So we have to remember that density equals mass divided by volume and mass by proxy equals density times volume. So the concentration of our air Is 100 mg per kilogram of air. Our volume of air equals r length times width times high, Which in this case is 4.0 m Times 5.5 meters, Times 3.5 m Equals 77 m Cube. So our massive air equals 77 m cubed, times one centimeter Over to the negative 2nd m. And that is all cubed Times 0.0012, 25g over centimeters cubed. So our meters cubed are canceling out and our centimeters cubes are canceling out. And that gives us 94, 325 grams of air. So now we need to solve for our mass of hydrogen sulfide, Which equals grams of air times one kg Over to the 3rd g times milligram of hydrogen sulfide divided by kilograms and our grams of air canceling out and our kilograms of air canceling out? And that gives us 32.5 mg of hydrogen sulfide. And now we're going to put it in scientific notation. So we want to move our decimal over 123 spots and we want to round and because for To the right of it, the number is less than five, So it will stay at four. So 9.4 Times 10 to the 3rd milligrams of hydrogen sulfide. And that is our final answer. Thank you for watching. Bye.