Human blood gives rise to an osmotic pressure of approxi-mately 7.7 atm at body temperature, 37.0 °C. What must the molarity of an intravenous glucose solution be to give rise to the same osmotic pressure as blood?

Video transcript

Hello. Everyone is in this problem given the automatic pressure of red blood cells and 7.38 A. T. M. And we're being asked what the majority should be of the white blood cell solution to have the same osmotic pressure as our red blood cells. So for our equation here we're using that pi is equal to capital M. R. T. So what this stands for is the automatic pressure. Capital M. Here is polarity. The capital R. Here is our ideal gas constant. You can actually write this out as well since we'll be using it later Anyways, that is 0.8206 units being leaders times A tm over moles times kelvin. So all the units in this equation should follow this ideal gas law units. And now for capital T. Here, that's just temperatures and kelvin's. So we want to find the polarity. So we're gonna go ahead and isolate this capital M. If we do so, and rearrange this equation, we get that capital M similarity is equal to the osmotic pressure over R times T. All right. So, we see here, since we have the temperature and the pressure, the pressure does have the correct units, but the temperatures does not. So for 25°C, we can convert this into Kelvin's by simply adding 273 so that some is 298 Kelvin's and this is our t. So temperature. So now plugging all the information into this equation here, we get that similarity is equal to The pressure is 7.38 a. t. m. And then our deal gas constant, which has brought it out in blue is 0.8 to 06 units being A. T. M. Times leader over mold times Calvin. And then we need to multiply all of this by team, which is 298 Calvin's. You see now the A. T. M. Will cancel and Calvin's will cancel. So once you put everything into the calculator, you get the numerical value Of 0.3018 and units being moles per liter, which is the exact units for the units of concentration of malaria T. So this right here is going to be my final answer for this problem.