Video: Calculating Concentrations from Masses and Volumes

Which of the following aqueous solutions has a molarity of 1.0 M? [A] 40 grams of HF dissolved to make 2.5 liters of solution [B] 48 grams of LiOH dissolved to make 2.0 liters of solution [C] 62 grams of Na₂O dissolved to make 0.75 liters of solution [D] 73 grams of HCl dissolved to make 1.25 liters of solution [E] 180 grams of C₆H₁₂O₆ dissolved to make 1.5 liters of solution

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Video Transcript

Which of the following aqueous solutions has a molarity of 1.0 molars? A) 40 grams of HF dissolved to make 2.5 liters of solution, B) 48 grams of LiOH dissolved to make 2.0 liters of solution, C) 62 grams of Na₂O dissolved to make 0.75 liters of solution, D) 73 grams of HCl dissolved to make 1.25 liters of solution, or E) 180 grams of C₆H₁₂O₆ dissolved to make 1.5 liters of solution.

For each of these statements, we’re going to need to take the mass of the compound given and work out the amount in moles. To do that, we’re going to divide the mass in grams by the molar mass in grams per mole. We’ll then take the amount of each substance in moles and work out its concentration. We’ll do that by dividing by the volume in liters. The unit molar simply means moles per liter. At the end, we’ll find the solution with a molarity or concentration of 1.0 molars.

So let’s get cracking with A. We’re dealing with fairly round numbers. So we can use these simplified atomic masses of the elements. The rounded relative atomic mass of hydrogen is one. And the relative atomic mass for fluorine is 19. So the molar mass of HF, hydrogen fluoride, is one plus 19 grams per mole. We can work out the number of moles of hydrogen fluoride in 40 grams of hydrogen fluoride by dividing 40 grams by 20 grams per mole, giving us two moles of hydrogen fluoride. We can then work out the concentration by taking the number of moles of hydrogen fluoride and dividing it by our volume in liters, 2.50. This simplifies to 0.8 molars. 0.8 isn’t 1.0. So A is not a correct answer.

The relative atomic mass of lithium is about seven. And the relative atomic mass of oxygen is about 16. So the molar mass of LiOH, otherwise known as lithium hydroxide, is seven plus 16 plus one grams per mole, which evaluates to 24 grams per mole. We can calculate the amount of moles of lithium hydroxide in 48 grams of lithium hydroxide by dividing 48 grams by the molar mass, 24 grams per mole, giving us two moles. We can then calculate the concentration in molars by dividing the amount in moles by our volume in liters. This gives us 1.0 molars. So our correct answer is B: 48 grams of lithium hydroxide dissolved to make two liters of solution will have a molarity of 1.0 molars. But let’s check the others just in case.

Sodium has a relative atomic mass of 23. So the molar mass of Na₂O, otherwise known as sodium oxide, is two times 23 plus 16 grams per mole, giving us 62 grams per mole. We get the amount of sodium oxide in 62 grams by dividing 62 by 62 grams per mole, giving us one mole. Dividing one mole by our volume in liters, 0.75, gives us 1.3 recurring molars. So that’s definitely not the right answer.

Chlorine has a relative atomic mass of about 35.5. So the molar mass of HCl is equal to one plus 35.5 grams per mole. We can work out the amount of HCl in moles in 73 grams of HCl by dividing 73 grams by the molar mass, 36.5 grams per mole, giving us two moles. Dividing two moles through by 1.25 liters gives us a molarity of 1.6 molars.

So one left to go: C₆H₁₂O₆ is the molecular formula for glucose. But it’s also the molecular formula for many isomers of glucose. Carbon has a relative atomic mass of 12. So the molar mass of C₆H₁₂O₆ is six times 12 plus 12 plus six times 16 grams per mole. That’s 180 grams per mole. This means in 180 grams of C₆H₁₂O₆, we have one mole, meaning for one point liters of solution, we have a concentration of 0.6 recurring molars.

That’s all the other statements accounted for, meaning that of the five aqueous solutions given, the only one with a molarity of 1.0 molars is 48 grams of lithium hydroxide dissolved to make two liters of solution.

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