A saturated solution of an ionic salt MX exhibits an osmotic pressure of 74.4 mm Hg at 25 °C. Assuming that MX is completely dissociated in solution, what is the value of its Ksp?

Video transcript

Hey everyone, we're told at 25 degrees Celsius, a solution of magnesium carbonate exerts an osmotic pressure of 97. millimeters of mercury. Given complete dissociation of magnesium carbonate, calculate the soluble itty product constant of magnesium carbonate first. Let's go ahead and write out our reaction. So we have magnesium carbonate and this is in its solid state. This will lead to the dissociation of our magnesium ion with a two plus charge And our carbonate ion with a -2 charge. As we can see right here, our Van Hoff factor, which is the number of moles of particles formed in solution, per mole of solute is going to be too. Now writing out our K. S. P. Which is our scalability product constant. This will be the concentration of our magnesium ion times the concentration of our carbonate ion. Now we're going to go ahead and use our formula for osmotic pressure to determine our concentration. So as we've learned, it's going to be our osmotic pressure is equal to our Van Hoff factor, times our polarity times our ideal gas constant, times our temperature solving formal clarity, we get our osmotic pressure divided by our Van Hoff factor divided by our ideal gas constant, divided by our temperature. Now let's go ahead and plug in our values. So we had 97.12 mm of mercury. But since our gas constant is in atmospheric pressure, we can go ahead and use dimensional analysis to convert this and we know that we have 760 of mercury per one atmospheric pressure. Next we're going to go ahead and divide this by our van Hoff factor, which we determined to be two Times Our Ideal Gas Constant, which is 0.08206 leaders times atmospheric pressure divided by Mole Times Kelvin. Next we're going to add in our temperature. So we were told we were at 25°C But since we want this to be in Kelvin, we're going to add 273.15. Now when we calculate this out and cancel out our units, We end up with the polarity of 2.61155 times 10 to the -3 Molar. Now that we have our concentration, let's go ahead and plug this into our soluble itty product constant. So we're going to multiply 2.61155 times 10 to the negative three times 2.61155 times 10 to the negative three. Since this is the concentration of both magnesium and our carbonate ion. When we calculate this out, we end up with a solid ability product constant of 6.8-0 times 10 to the -6, which will be our final answer. Now I hope that made sense. And let us know if you have any questions