Uric acid, the principal constituent of some kidney stones, has the formula C₅H₄N₄O₃. In aqueous solution, the solubility of uric acid is only 0.067 g/L. Express this concentration in (m/v)%, in parts per million, and in molarity.

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Welcome back everyone. The main component of the crystals and taro that causes itching is calcium oxalate. The solubility of calcium oxalate in water is 6.66 times 10 to the negative third power grams per liter at room temperature. What is the concentration in mass by volume percent in parts per million and in molar? So beginning with our mass by volume percent calculation recall that the unit should be in grams per milliliter. And so we're given our solubility of calcium oxalate C AC equal to 6.66 times 10 to the negative third power grams per liter. And we want to multiply by a conversion factor to go from leaders in the numerator to milliliters in the denominator where we should recall that our prefix Milly tells us that we have an equivalence of 10 to the negative third power of our base unit leader in the numerator, canceling out our units of leaders. We're left with grams per milliliter and will now have our solubility as 6.66 times 10 to the negative sixth power gramps per milliliter. And based on our mass percent by volume calculation we're going to need to interpret this in terms of grams per 100 mL of solvent. So we would multiply our solubility by a conversion factor to go from 100 mL in the numerator to one mL in the denominator. So, canceling out and sorry, not canceling out but placing parentheses and taking this calculation in our calculators, this will simplify to our solubility as now 6.66 times 10 to the negative fourth power grams per 100 mL of solvent. And we can cancel out the milliliters here so that we have just grams per milliliter as our final units. Now moving back to our mass by volume percent calculation recall that it represents the mass of our solute Divided by our volume of our solution multiplied by 100%. So in this case, we would plug in for our numerator, our mass of our solute as 6.66 times 10 to the negative fourth power grams of calcium oxalate divided by our volume of our solution being 100 mL in terms of the mass by volume percent. And then we're going to multiply this quotient in parentheses by 100%. And this is going to simplify to our mass by volume percent equal to 6.66 times 10 to the negative fourth power percent mass by volume. Next, let's move on to calculating our concentration in parts per million where we should recall that we would find this by taking the mass of our solute calcium oxalate divided by the mass of our solution, which is then multiplied by a power of 10 to the sixth. We want to make a note that our solubility equal to 6.66 times 10 to the negative third power grams per liter is very small. And so therefore, we're going to assume that our density of our solution of calcium oxalate is equal to the density of water. So row of the solution is equal to row of water. And recall that the density of water is equal to 1.0 g per milliliter. And this assumption is important because it allows us to understand that the mass of dissolved calcium oxalate in the water is negligible compared to the mass of water itself. So it's going to have a very minimal impact on the overall mass and density of our solution. So to make our calculation for parts per million simple, we can just take our solubility 6.66 times 10 to the negative third power grams per liter. And we can just directly multiply to go from leaders in the numerator to milliliters in the denominator where again, we have for one mL in the denominator, an equivalence of 10 to the negative third power leaders. So now canceling out leaders, we are left with grams per milliliter of calcium oxalate and we can just we'll get a result of 6.66 times 10 to the negative sixth power. And now we can just multiply by our power of 10 to the sixth. And this is going to give us our Solubility concentration in parts per million as 6.6, 6 parts per million. So, so far we've come up with our first two answers, our concentration of calcium oxalate in parts per million. And then our mass by volume percent of calcium oxalate in mass by volume percent again as 6.66 times 10 to the negative fourth power. Now moving on to our third calculation which is to calculate the molar of this concentration. Recall that polarity is expressed in units of moles per liter. So we need to calculate first the molecular weight of our calcium oxalate In which from our periodic table, we find our massive calcium as 40.07, 8 g per mole. This is added to our mass of carbon in which we have two atoms of carbon, Which will be multiplied by the molar mass of carbon from the periodic table as 12.01 g per mole. I'm sorry, this should say two moles of carbon. So plus two moles of carbon times the mass of carbon molar mass of carbon. 12 point oh one g per mole. Then added to this, we have our four atoms or four moles of oxygen multiplied by oxygen's molar mass from the periodic table at 16.0 g per mole, canceling out moles. We're left with units of grams and we find our molecular weight of calcium oxalate equal to 128.0, 98 grams per mole. So now going into our calculation for molar, we have the solubility of calcium oxalate given from the prompt again as 6.66 times 10 to the negative third power grams per liter. And we need to introduce moles. And so we're going to multiply it by a conversion factor to go from grams of calcium oxalate in the denominator to moles of calcium oxalate in the numerator. Where from our molar mass, we can say that for 128.0 g of calcium oxidate oxalate. We have in our numerator, one mole of calcium oxalate. And so canceling out grams of calcium oxalate. We're left with moles of calcium oxalate per liter as our final units for molar. And we find our molar equal to the value of 5. times 10 to the negative fifth power molar. And this would be our third final answer as our molar of our calcium oxalate. So all of our final answers highlighted in yellow correspond to choice c in the multiple choice as the correct answer, which states that our mass by volume percent of calcium oxalate is 6.66 times 10 to the fourth power percent. Our parts per million is 6.66 parts per million. And then we have 5.20 times 10 to the negative fifth power molar. So I hope that this made sense and let us know if you have any questions.

Uric acid, the principal constituent of some kidney stones, has the formula C₅H₄N₄O₃. In aqueous solution, the solubility of uric acid is only 0.067 g/L. Express this concentration in (m/v)%, in parts per million, and in molarity.

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