Which of the following solutions has the higher osmolarity?

Question

b. 0.30 M NaOH or 3.0% (m/v) NaOH

Accepted Answer

Welcome back, everyone. Calculate the osmolarity of the following solutions and determine which is higher. We're comparing 5.0 mass by volume percent of calcium hydroxide or 0.750 molar calcium hydroxide. Let's recall that calcium hydroxide C A parentheses. Oh Sub two is an ionic compound where hydroxide is our poly atomic ion which transfers electrons to our calcium two plus caton. And so being an ionic compound and having the transfer of electrons, this is going to be considered a salt and based on our solubility rules, this will fully dissolve into the following ions where we form our calcium two plus C as well as our hydroxide anion. And in order for this to be a balanced equation, notice that we have two moles of hydroxide on the reactant side. So we'll place a coefficient of two in front of our hydroxide on the product side. And this means that calcium hydroxide forms three moles total of ions where we have one mole of our calcium two plus ion and two moles of our hydroxide anion. With this outline. Let's next recall that for osmolarity, it's going to be a measure of our total concentration of solute part particles in a solution. And recall that our units for osmolarity are typically in O Os M per liter or osmo per liter. So again, this is our unit. So let's begin with our first solution where we're given 5.0 mass by volume percent of calcium hydroxide. And let's recall that for a mass by volume percent, we will interpret it as equivalent. And so we'll put an equal sign actually to 5.0 grams of calcium hydroxide per 100 mL of solution. So notice that we have units of grams per milliliter. And we want to convert this to a molar concentration which we recall is interpreted as moles per liter. And from moles per liter, we can multiply by our molar ratio of our ions from the solubility of calcium hydroxide or dissolution rather, since it's a solid and using that molar ratio as a conversion factor will lead us into our final unit of osmoles per liter. So let's take these steps. So what we have is we want to note down the molar mass of calcium hydroxide. And from our periodic table, we would see that we have a molar mass of 74.0 93 g per mole. So beginning with our mass by volume percent ratio, we have 5.0 g of calcium hydroxide for or per 100 mL of solution. So to begin by canceling out our grams in the numerator, we're gonna multiply by the conversion factor being our molar mass where we understand that for 74.0 93 g, we have in our numerator, one mole. And so now we can cancel out our unit of grams. And we're left with moles per milliliter in which we can now multiply by our molar ratio between our ions. So we want to multiply by and sorry correction. I actually skipped a step. So we need to convert to molar, as we stated right now, we have moles per milliliter. So we need moles per liter. So we're gonna cancel out milliliter by multiplying by the next conversion factor. Where in our numerator, we understand that our prefix Milly tells us that we have an equivalent of 10 to the negative third power of our base unit leader in its nominator. So canceling out milliliters, we now have moles per liter, which again is interpreted as molar. And this gives us a molar concentration of calcium hydroxide as 0.6748 moles per liter or molar of calcium hydroxide. And now we want to convert this to os moles per liter. So we're gonna start with our calculation. So let's define this first step. We just went through as step one and this next step is step two. So we're gonna start with our result from step one as 0.6748 moles per liter of calcium hydroxide. And we're going to multiply to go from moles of calcium hydroxide in the denominator, two moles of ions in the numerator. And from our balanced equation, we understood that for one mole of calcium hydroxide, we form three moles of dissolved ions in our numerator. And so canceling out moles of calcium hydroxide. We now have moles per liter or sorry, moles of ions per liter to be more specific. And since our moles of ions are dissolved, so there are solute particles that will be equivalent to osmoles per liter. And so we would get as a result in our calculators, the value 2.02 moles of ions per liter, which is equivalent to 2.02 os moles per liter. And this would be our first answer or actually, we need to compare them. So we're gonna move on to our second calculation which is to convert 0.750 molar of calcium hydroxide to osmoles. And so this first value that we found 2.02 osmoles per liter would be our osmolarity of calcium hydroxide from the 5.0 mass by volume percent. And now for our second calculation, we begin with 0.7 50 moles per liter of calcium hydroxide in our denominator. And we can directly multiply by our molar ratio. Where in our denominator, we have moles of calcium hydroxide. And in our n, we have moles of our dissolved ions, our solute where we said that we have one mole of calcium hydroxide which dissolves three moles of ions in the numerator. So, canceling out moles of calcium hydroxide, we're left with moles per liter moles of ions per liter, which again is equivalent to osmolarity. And this calculation will result in a value of 2.25 moles of ions per liter, equal to 2.25 osmoles per liter as our osmolarity of our 0.7 50 molar calcium hydroxide. And so we can say that because 2.25 osmoles per liter is greater than 2.02 osmoles per liter. Therefore, our 0.750 molar solution of calcium hydroxide has a higher osmolarity. Then compared to our 5.0 mass by volume percent of calcium hydroxide solution, and our final answer will correspond to choice a in the multiple choice. So I hope that this made sense and let us know if you have any questions.

Which of the following solutions has the higher osmolarity?
b. 0.30 M NaOH or 3.0% (m/v) NaOH

Key Concepts

Osmolarity

Molarity

Mass/Volume Percent Concentration

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