 Let's do this problem. It says, biochemists have discovered more than 400 mutant varieties of hemoglobin, the blood protein that carries oxygen throughout the body. A physician studying a variety associated with a fatal disease first finds its molar mass. She dissolves 21.5 mgs of the protein in water at 5 degrees Celsius to make 1.50 mls of solution and measures an osmotic pressure of 3.61 tor. What's the molar mass of this protein? So the first thing we need to do or think about is, well, what is the equation for the osmotic pressure? So when we do that, we know pi equals molarity times the gas constant times t. So, well, we don't have molarity. That's what we're looking for. The gas constant I've written down here already for you. And t is right here. But t is not in the appropriate units. So we're going to have to convert that. So in order to do that, we just put 273 add 273 to it. We can calculate. So 278.0, I guess, let's put 278. OK, so let's rearrange this equation to solve for molarity. So molarity equals pi divided by RT. Everybody OK with that? OK. But pi here is in units of tor, right? So we're going to have to convert that before we do anything as well. So do you remember the conversion factor between tor and 760 to 760? Yeah. 7, 5 times. So we've got pressure in the right units. We've got temperature in the right units. So let's go ahead and figure out what the molarity of this is. So I like to do this for you guys kind of the baby way where you break up everything into dividing bit, right? So let's just do that. 0.0821 liter ATM per 1 mole kelvin. So you can see what our units are going to be eventually where they cancel out. And then we're going to multiply this by 278.1 or 0.0 whatever you got, kelvin. So cancel, cancel there. Leaders are nothing divided by leaders divided by moles. Is moles per liter? Is everybody OK with that? I wonder. So let's go ahead and plug in Chubb now. So divided by 0.0821. We're going to divide that by 278. And just to make sure, right? Molder. OK. So as you guys remember, what molar is here? So that's moles per liter, right? So remember, we're looking for the molar mass of this thing. So we still got to figure out, well, what is the number of moles, right? So this is moles per one liter like that. So the molar mass is going to be the number of moles or the number of grams per mole, right? So let's write that down over here per mole. So notice, we've got grams here or milligrams, which we can convert to grams. Is everybody OK with that? And we've got moles here. But this is moles per liter. Did we have a liter solution? 1.5 mils, right? So 1.5 mils. So we're going to have to figure out, well, how many moles, this is how many moles is in a liter? Are we going to figure out how many moles is in 1.5 mils? Is everybody OK with what I'm saying? Wonderful. So you want to remember one liter, 1,000 mils times 1.5 mils, like that, right? If we cancel, cancel, cancel, cancel, that should give us the number of moles of protein. Is everybody OK with that? OK, so let's do that. Divide it by 1,000 times 1.5. OK, so the number of moles of protein we have is 3.12 times 10 to the negative 7 moles. Got that? Moles of protein. Wonderful. So now I'm actually going to have to erase some of this. I'll have enough space on the board to continue. Can I erase this part of the board? Would anybody have any problem with that? So the mass of the protein is given to us in milligrams here. But we want that in grams, right? OK, so the mass of the protein in grams is going to be 1,2,3, right? So 0.0215 grams, like that. Is everybody OK with that? OK, so do we have the grams of the protein now? How many grams we got? Do we got how many mils we got? Help me out. Do we have those things? Yes, we do, right? Is that all we need for the molar mass? So now let's just plug each other. OK, so molar mass equals the grams, which is this. 0.0215 grams divided by the number of moles. 3.12 times 10 to the negative 7 moles. OK, and it's a protein, right? And so for all you biologists, would you expect that to be a very high molar mass or a very low molar mass? Very, very high, very high. So let's see what it is. So 0.0215 divided by the answer. And I get something that's 6.89 times 10 to the 1,2,3,4. 4 grams per mole. Pretty big molar mass. Any questions on that one? I know there was a lot of steps, OK? So watch out about all the steps. Just make sure you're solving for the things you're solving for, OK? So you know what molar mass is. Look for a number of moles. Look for grams, things like that, OK? Questions before I kill it? Wonderful.