The specific volume of solid ammonium sulfate is 0.565 ml/g. The solubility of ammonium sulfate at 0 oC is 706 g/1000 g water. Calculate the concentration of ammonium sulfate in a saturated solution at 0 oC.
how can i solve this question ???
my mind is blowing!!!
I can show you how to estimate it, and it will be a very close value to the true value, but I don't think this is valid if you want a more exact value. I'll explain later.
mols (NH4)2SO4 = g/molar mass = 706/132.14 = 5.343 mols.
specific volume = 0.565 mL/g
0.565 mL/g x 706 g = 398.9 mL INCREASE in volume
We have 5.343 mol/1000 g H2O. Assuming density of water @ zero C is 1.0, that is 5.343 mols/1000 mL. If we add 706 g (NH4)2 SO4 to that we now have a volume of 1000 mL + 398.9 mL = 1398.9 mL or 5.343 mols/1.3989 L = 3.8 M. The literature says it is 3.9 M for a saturated solution @ zero C. My problem with this calculation is that specific volume is mL/g. I think that means mL OF THE SOLID per g of the solid. I do not think it means that increases the volume of a solution that much. For an estimation it is OK but we know that when a solid is added to water that the volume of the SOLUTION, may decrease, increase, or stay the same. In separation of proteins by making them coagulate with saturated solutions of (NH4)2SO4 they use the procedure I've outlined above but I don't think that process gives them an accurate value for M. Close, I think, but not exact. It could be argued that specific volume DOES MEAN mL increase when added to a solution; however, every definition of specific volume I've read says that it is the reciprocal of density. So if I take 1/0.565 I get about 1.77 g/mL. That solution would be composed of 1000 g H2O + 706 g of the salt for 1706 g solution and 1706/1.77 = about 964 mL. Then 5.34 mols/0.964 L = about 5.5 M and that isn't even close to 3.9 M. So I'm thinking that (NH4)2SO4 works out that way, that makes a very easy way to get a very close estimate. Hope this helps.
Thanks So Much....
To solve this question, you can use the formula for concentration:
Concentration (C) = mass of solute (in grams) / volume of solvent (in liters)
Step 1: Convert the volume of solid ammonium sulfate from mL to liters.
Given: specific volume of solid ammonium sulfate = 0.565 mL/g
To convert mL to liters, divide by 1000:
Specific volume of solid ammonium sulfate = 0.565 mL/g = 0.565/1000 L/g
Step 2: Determine the mass of solid ammonium sulfate dissolved in 1000 g of water.
Given: solubility of ammonium sulfate at 0 °C = 706 g/1000 g water
To calculate the mass, we can assume that 1000 g of water is equal to 1000 mL of water (since the density of water is approximately 1 g/mL). So the mass of the solute in 1000 g of water is 706 g.
Step 3: Calculate the concentration of ammonium sulfate.
C = mass of solute / volume of solvent
C = 706 g / 0.565 L
Calculating this, we get:
C = 1247.79 g/L
The concentration of ammonium sulfate in a saturated solution at 0 °C is approximately 1247.79 g/L.
To solve this question, you need to use the given information and formulas for concentration and specific volume. Here is the step-by-step process:
Step 1: Calculate the mass of ammonium sulfate in the saturated solution at 0 oC.
The solubility of ammonium sulfate at 0 oC is given as 706 g/1000 g water. This means that for every 1000 g of water, 706 g of ammonium sulfate can dissolve. So, let's assume we have 1000 g of water. Therefore, the mass of ammonium sulfate in the saturated solution would be 706 g.
Step 2: Calculate the volume of the saturated solution.
To find the volume of the solution, divide the mass of ammonium sulfate by its specific volume. The specific volume of solid ammonium sulfate is given as 0.565 ml/g. So, using the mass of ammonium sulfate (706 g), you can calculate the volume as follows:
Volume = mass / specific volume
Volume = 706 g / 0.565 ml/g
Volume ≈ 1247.8 ml
Step 3: Calculate the concentration of ammonium sulfate in the saturated solution.
Concentration is defined as the amount of solute divided by the volume of the solution. The amount of solute is given as the mass of ammonium sulfate (706 g). Therefore, the concentration can be calculated as follows:
Concentration = mass of solute / volume of solution
Concentration = 706 g / 1247.8 ml
To get the concentration in standard units, you can convert milliliters to liters:
Concentration ≈ 706 g / 1.2478 L
Concentration ≈ 565.2 g/L
So, the concentration of ammonium sulfate in the saturated solution at 0 oC is approximately 565.2 g/L.