The osmotic pressure of a saturated solution of strontium sulfate at 25 C is 21 torr. What is the solubility product of this salt at 25 C?

Video transcript

Hi everyone. This problem reads at 27 degrees Celsius. A saturated solution of magnesium carbonate has an osmotic pressure of 98 Tour, calculate its soluble itty product constant at this temperature. Okay, so our goal here is to calculate the K. S. P. Value. And in the problem we're given the temperature and we're given the osmotic pressure. So in order to solve this problem, we need to start off by calculating the molar concentration and the molar concentration is going to be equal to the osmotic pressure over gas constant. R times T. Okay, so let's take a look at what we already have in the problem. We have the osmotic pressure and we have the temperature R is a constant and that constant is 0.8206 Leaders times A. T. M. Over mo times kelvin. So, we need to pay attention to units and make sure the units match. Okay, so for our osmotic pressure it was given in tour. Okay, So we have 98 Tour. So we need our tour and A T. M. Okay, So we need to convert this. So 1 80 M is equal to 760 Tour. All right, so making sure our unit's canceled towards cancel and we're left with a final answer of 0. 80 M. Secondly in r gas constant. R temperature is in kelvin. But the problem gives us our temperature as 27 degrees Celsius. So, we need to go from 27 degrees Celsius to kelvin. And we do that by adding 273.15. Okay, so with that we get a temperature of 300.15 Kelvin. So now we can go ahead and plug these units in. So our osmotic pressure is 0.1289. R. R. Gas constant is 0.8 to 06. Leaders times a tm. Over mole times kelvin. And our temperature is 300.15 kelvin. So because we're looking for similarity or molar concentration when our units cancel, that should be the only unit we're left with. So a T M's cancel, kelvin cancels. Okay, so here we have moles over a liter. Alright and that is concentration osmolarity. So we get a mill arat e equal to 5.2353 times 10 to the negative five. Alright, so with that let's go ahead and write out our reaction. Okay, so we have magnesium carbonate and it dissolves into its ions. Alright, so one mole of magnesium carbonate that dissolves produces two moles of ions. And here we need to take note of moller solid ability because our end goal here is to calculate scalability product constant. We need to take note of moller scalability for moller solly ability. The concentration of the ions is going to equal each other. Okay so that means our concentration of ions is going to equal what we calculated above times 10 to the negative five. So if we want to know that individual concentrations, we need to divide this by two. Okay. And when we divide by two we get 2.6177 times 10 to the negative three. Alright. So what that means then is r K S P. Or our solid ability product constant is going to equal this number that we just divided by two but it's going to be squared. Okay? So that means our final Ks p value is going to be 6.8521 times 10 to the negative six. And this is our final answer for the solid ability product constant. That's it for this problem. I hope this was helpful.