In a given diffusion apparatus, 15.0 mL of HBr gas diffuses in 1.0 min. In the same apparatus and under the same conditions, 20.3 mL of an unknown gas diffuses in 1.0 min. The unknown gas is a hydrocarbon. Find its molecular formula.

Video transcript

Hey everyone. So under the same conditions We have 20 ml of krypton gas and it's gonna diffuse in 1.5 minutes and then we have 16 ml of an unknown hydrocarbon Which is gonna diffuse in one minute. And were asked to determine the molecular formula of the hydrocarbon. And we know that hydrocarbon means it contains carbon and hydrogen. We need to first calculate the rate of infusion to the right of krypton, Gonna be the volume which is 20 ml By the time, which is 1.5 minutes. And this will give us 13 0.3 milliliters per minute. And then for the right of unknown hydrocarbon which we'll call X. It's going to be 16 male leaders about about one minute. Would you give us 16 milliliters per minute? So now we need to use Graham's Law of effusion to find the molar mass of the hydrocarbon. And recall that this is rate a divided by rate. Be take it to the scare route. The molar mass of B. The molar mass of a. So in this case it's gonna be the rate of krypton gas. Find by the rate of the unknown hydrocarbon which is X. Into the square root the mother mass of the owner hydrocarbon right by the molar mass of krypton gas. Now if we plug in our values, we're gonna have 13.3 divide by even to the Mueller mass of the heart of carbon, which we don't know About about 83 .798. So now if you square both sides, We're gonna get 0.69, you get to the Mueller mass of the hydrocarbon About about 83 . 0.69 in 83 .798. Does he give us the Mueller mass of the hydrocarbon? For the miller mass? The hydrocarbon. It's 58 grams per mole. So now that we have the molar mass, we need to find the number of carbon and hydrogen in the formula. So we can say X is equal to the number of carbon. And why is it to the number of hydrogen? We're gonna have the muller mask carbon which is 12 times X. Plus the molar mass of hydrogen, which is one thomas Y decided equal to 58 which is a total mass of the hydrocarbon. And now we can solve for X. So we subtract one Y. From both sides, We get 12 x 58 minus one Y. And if we divide both sides by 12, We're gonna get x equals 4. -0.083. Why? So now we can plug this into the equation for X. And solve for Y. They're gonna get 12 Times 4.83, 0.083. Why plus one? Y. It goes 58. Then we can have 57. -0.996. Why plus one Y. It goes 58. And it's a track both sides by 37 0.96. We're gonna get negative 0.996. Why plus one? Y. Equals 0.04. And then we have 0.004. Why? It goes 0.04. And we're gonna buy both sides by 0.004. So we get wide, it goes 10. So this is gonna be the number of hydrogen we have in the hydrocarbon. So now we can play intent for Y and solve for X. We're gonna have 12 x Plus one times You go 58. So this is 12 x Plus 10 equals 58. It was a track 10 on both sides And get 12 x equals 48. So we divide both sides by 12, You get x equals four. And this is the number of carbon and hydrocarbon. So our molecular formula is going to be c. four, age 10. Thanks for watching my video. And I hope it was helpful.