Desert countries like Saudi Arabia have built reverse osmo-sis plants to produce freshwater from seawater. Assume that seawater has the composition 0.470 M NaCl and 0.068 M MgCl2 and that both compounds are completely dissociated. (b) If the reverse osmosis equipment can exert a maximum pressure of 100.0 atm at 25.0 °C, what is the maximum volume of freshwater that can be obtained from 1.00 L of seawater?

Video transcript

Hi everyone for this problem it reads Israel has built plants that turn seawater into freshwater, calculate the maximum volume of fresh water that can be obtained from 1.25 L of seawater if the reverse osmosis equipment in the plant exerts a maximum pressure of 105 atmos assume that seawater is composed only of 0. molar sodium chloride and 0.7 to moller calcium chloride which are completely dissociated. And that the temperature of the water is only 25 degrees Celsius. So the question that we want to answer here is the maximum volume of fresh water that can be obtained. Okay. And we're comparing this to seawater and let's go ahead and take a look at what we have. So we have sodium chloride and we also have calcium chloride. So let's go ahead and count how many ions we have. Okay, so for sodium chloride we'll say that I equals two. And for calcium chloride the number of ions is equal to three. Alright, so step one to solve this problem is we're going to calculate the similarity given that the osmotic pressure is atmospheres. And the equation that we're going to use to do this is osmotic pressure is equal to malaria. T times gas constant. R times temperature. And so we want to we want to solve for similarity. So let's go ahead and isolate this variable. We'll divide both sides by R. T. And what we'll get is malaria T. Is equal to osmotic pressure over R times T. So let's just write out the variables that are given in the problem. Okay, so the osmotic pressure is given and that value is 105. atmospheres Gas constant R. is a value we should have memorized which is 0.08206 leaders atmosphere over mole Kelvin. And the temperature given in the problem is 25°C. But we need to convert this to Kelvin to match the units or to match the temperature unit in our gas constant. So we'll add 273.15 here to convert it to Kelvin. And what we'll get for temperature is 298. Kelvin. So now we have everything we need. So let's go ahead and plug these values in to solve four polarity. So osmotic pressure is 105.0 atmospheres gas constant. R. is 0.08-0 six leaders atmosphere over Mole Kelvin and temperature is 298.15 Kelvin. Okay, so let's go ahead and do this calculation. And when we do we're going to get the malaria T is equal to four 0.291637 moles per liter because that is what malaria T translates to. Okay, so now step two is we're going to calculate the volume, the maximum volume of fresh water. Okay, so the way that we're going to do this is by using the equation. M one times V one is equal to M two times V two. Okay, and here we're interested in calculating V one. Okay, we're gonna let V one equal, are We're going to let V1 equal the volume of our given. Okay, so Let's go ahead and isolate this variable. And what we're going to get is V one is equal to M2 times v two over M one. Okay, so Armel arat E. So we're going to let let's define these variables. We're going to let. So we're calculating V one. So V one is our question mark. Okay. And we're going to let em one Equal what we just calculated for a malaria t. Okay, so this is 4.291637. Move per leader. Okay. And we're going to take M two and V two as the malaria T and volume of seawater which is composed of 20.540 molar sodium chloride and 0.7 to moller calcium chloride. So when we do this, what we're going to do is we're going to take the ions and multiply it by the mill arat E for both sodium chloride and calcium chloride. So what this is going to look like is we're going to have two ions. Let's do this in a different color. We're going to have two ions. So this is for our sodium chloride. Times the modularity. So 0.540 mo per liter plus Three ions times the modularity of the calcium chloride, which is 0.072 mol per liter. And this is going to be multiplied by 1. liters. Okay, Because in the problem it's asking us to calculate the maximum volume from 1.25 liters of seawater. So we're going to now multiply this by 1. liters. Okay, So let's just move this over since it is cutting off. All right. So what we're going to and then this is gonna be divided by M1 where M1 is 4. 1637 more per leader. Okay, So we've plugged everything in. So let's go ahead and solve for V one. So when we solve for V1, it's 0.3774, 0. 78 leaders. Okay, so a volume of 1.25 liters of seawater can be reduced to this number. So it can be reduced 2.377478 liters by osmotic pressure of 105 atmospheres. So that means the volume of fresh water that can be produced is going to be the difference. Okay, so we're going to take one point 25 liters and subtract the value we just calculated which is 0.377478 liters. And this gives a answer of 0. to 5 to two liters. Okay, so this is going to be our final answer here. 0.87 to 5 to two. And let's go ahead and Put this in six fake. So we have 0.87 L as our final answer. And this is going to be the volume of fresh water that can be produced. That is it for this problem? I hope this was helpful.