If you had only 23 g of KOH remaining in a bottle, how many milliliters of 10.0% (m/v) solution could you prepare? How many milliliters of 0.25 M solution?

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Welcome back everyone. If 20 g of sodium hydroxide has been weighed out, what is the volume in milliliters of 12.5% mass by volume solution that can be prepared? How many milliliters of 0.225 molar sodium hydroxide solution can be prepared from the same mass of sodium hydroxide. So we have a two part question prompt and we'll begin with the first question which is to find the volume and milliliters of the 12.5% mass by volume sodium hydroxide solution. We're going to start with the given mass of sodium hydroxide used of g to make the solution. And because we're starting with grams and we need millets to be our final unit. We're going to multiply by a conversion factor where we will interpret our mass by volume percent as in the denominator, 12.5 g of sodium hydroxide per 100 mL of solution. And so this will then allow us to cancel out our units of grams leaving us with milliliters for volume. And in our calculator, this will simplify to a volume of 160 mL of the 12.5% mass by volume sodium hydroxide solution. We're going to then convert this to scientific notation to form a number greater than one but less than 10 by moving the decimal 100.2 places to the left. And this will allow us to report the volume as now 1.60 times 10 to the positive second power milliliters of solution. So this would be our first answer 1.60 times 10 to the second power milliliters of solution from the 12.5% mass by volume sodium hydroxide solution. And so now we're going to then move on to part two of our prompt, which is determine the volume and milliliters of the 20. 25 molar sodium hydroxide solution prepared from the same mass. So we're going to start by determining the molar mass of sodium hydroxide. And let's recall that we would take the mass of sodium, sorry, the molar mass of sodium which makes up sodium hydroxide. And so that would correspond to a mass of 22.99 g per mole of sodium on the periodic table. Then we would add to this our mass of oxygen from the periodic table where we would observe, we have 16.0 g per mole of oxygen. And also in sodium hydroxide is hydrogen. And we would add the mass molar mass of hydrogen, which we should see is 1.8 g per mole of hydrogen on the periodic table. This will result in the molar mass of sodium hydroxide equal to 39.998 g per mole of sodium hydroxide in total. So now with the molar mass of sodium hydroxide, we're going to start with the mass of our sample given us 20 g of sodium hydroxide. And we're going to multiply to convert to go from grams in the denominator to moles in the numerator where we would incorporate that determined molar mass as 39.9 98 g of sodium hydroxide per mole, one mole in the numerator. So now this allows us to cancel out our units of grams and we are at moles, but we need to get some milliliters. And so this is where we will multiply next to incorporate that given molar concentration, which is given as 0.225 molar and recall that molar is interpreted as moles per liter. And so we would multiply and interpret to go from moles in the denominator to then liters in the numerator where we would plug in 0.2 to five moles of sodium hydroxide in the denominator per one liter of solution in the numerator. So now canceling out moles, we would be left with liters, but we need to get two mL for volume. So we're going to then multiply to go from liters in the denominator to milliliters in the new meter where we would recall that our prefix millie tells us that we have an equivalence for one liter of 10 to the third power milliliters and canceling out liters. We're left with our final unit of volume in millis. And this will result in a volume equal to 2222.3 mL, which we can convert to scientific notation by moving the decimal point a total of three places to the left. And that's going to then result in the final answer equal to 2.22 times 10 to the positive third power milliliters of the 100.2 25 molar sodium hydroxide solution. And so our second final answer is 2.22 times 10 to third power milliliters of solution. I hope that this makes sense and let us know if you have any questions.

If you had only 23 g of KOH remaining in a bottle, how many milliliters of 10.0% (m/v) solution could you prepare? How many milliliters of 0.25 M solution?

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Key Concepts

Mass/Volume Percentage (m/v)

Molarity (M)

Stoichiometry