What is the molecular weight of a gas that diffuses through a porous membrane 1.86 times faster than Xe? What might the gas be?

Video transcript

Welcome back. Everyone determined the molecular weight and identity of a gas that diffuses 1.12 times faster than argon through a porous membrane. So we're going to recall that our rate of our gas is inversely proportional to the square root of its molar mass. This is what we want to recall as our rate of effusion, where our gas particles are traveling through a smaller hole, which is why the prompt mentions that we have a porous membrane here. So we're going to write out a relationship where the rate of our unknown gas. Sorry, let's say unknown gas here, divided by our rate of our argon gas is equal to our square root of the molar mass of our argon gas, Divided by our molar mass of our unknown gas. And according to our prompt, this quotient is equivalent to a value of 1.12. So, getting our molar mass of Argon from the periodic table, We see that this is equal to a value of 39.95 g per mole. So, incorporating this into our equation, we can say that the square root and sorry about that. So the square root of our molar mass of argon being 39.95 g per mole Divided by our molar mass of our unknown gas is equal to 1.12. And so simplifying this, we want to get rid of that square root term. So we're going to raise the right hand side of our equation to a power of two and the left hand side to a power of two, which will cancel out that square root term. And now we would simplify to 39. grams per mole, divided by the molar mass of our unknown gas equal to 1.2544. And because we have a diagonal here, we're going to just switch places with this value. And what we'll have is 39. g per mole, divided by 1.2544, which is going to result in A mass of 31.84 g per mole. Which we can round to about 32 g per mole. And so on our periodic table. When we find a atom with a molar mass of 32g per mole, we can think of oxygen, But we see oxygen on the periodic table has a molar mass of 16. And because oxygen is a diatonic molecule, it's going to have a molar mass of 32. And so we would say that our molecular weight of our gas, unknown gas is 32 g per mole. And the identity is going to be oxygen gas for the unknown gas. So what's highlighted in yellow is our final answer. I hope everything I explained was clear. If you have any questions, please leave them down below and I will see everyone in the next practice video