Concentration in Molarity: What it is and how to calculate it
Molarity is one of those terms that people like to talk about a lot when describing solutions. Unlike "unsaturated", "saturated", and "supersaturated", molarity is a numerical way of saying exactly how much solute is dissolved in a solvent. As you can probably tell from the section before, the term unsaturated or supersaturated can be applied to a wide variety of solution concentrations.
OK. Here's the definition of molarity:
Molarity is equal to the moles of solute divided by the liters of solution. To put it in the form of an equation:
(You will often see concentration given in “M” units. The “M” means moles/litre or mol/L. The IUPAC people – people that get paid to think about units – have decided that “M” is no longer an official unit because it makes calculations less straightforward, and that mol/L should be used instead. You will still see “M” in labs a lot, as old habits die hard. Just use mol/L in your calculations.)
OK. Quit freaking out. It's not that hard to figure out. Let's do an example:
Example: What's the molarity (a fancy way of saying concentration) of a solution that contains 5.5 moles of sodium chloride in 10.5 liters of solution?
Answer: concentration = moles / liters, or (5.5 moles) / (10.5 liters) = 0.52 mol/L, or 0.52 M
In this case, the unit is M, or mol/L. M stands for "molarity". A 0.52 M solution is referred to as being a "0.52 molar" solution. That's simple enough!
Sometimes these problems get a little bit harder. Instead of giving you moles, they give you grams. Instead of liters, they give you milliliters. Fortunately, you know how to do the necessary conversions. Here's a handy diagram to help you:
Let's do an example.
Example: If I have 3.50 grams of sodium chloride in 1250 mL of a solution, what's the concentration?
Concentration Worksheet
1)Explain why chemical compounds tend to dissolve more quickly in hot solvent than in cold solvent.
2)Give an example of two liquids that are immiscible (do not form a solution).
3)The pressure at the bottom of a lake is 2.35 atm. If water saturated with oxygen (concentration 0.34 g/L) is carried by a current to a depth where the solubility of oxygen is 0.21 g/L, what is the pressure of the water. (This is a tricky one. Use your gas laws to help you!)
4)How can you make a saturated solution from a supersaturated solution?
5)How can you make a supersaturated solution from a saturated solution?
6)How can you make an unsaturated solution from a saturated solution?
7)What is the molarity of a solution made when you dilute 35 grams of sodium carbonate to a volume of 3,400 mL?
8)Explain how you would make 450 mL of a 0.25 M calcium chloride solution.
Concentration Worksheet – Answers
1)Explain why chemical compounds tend to dissolve more quickly in hot solvent than in cold solvent.
The solvent molecules have more energy to pull the solute particles apart. If the heat of solution is greater than the heat required for breaking intermolecular forces (exothermic), then an increase in temperature would decrease solubility (rare). If the heat of solution is less than the heat required for breaking intermolecular forces (endothermic), then an increase in temperature would increase solubility (common).
2)Give an example of two liquids that are immiscible.
Oil and water.
3)The pressure at the bottom of a lake is 2.35 atm. If water saturated with oxygen (concentration 0.34 g/L) is carried by a current to to a depth where the solubility of oxygen is 0.21 g/L, what is the pressure of the water.
This is an application of your gas laws unit. Use Boyle’s Law, P1V1=P2V2
(2.35 atm)(0.21g/L) = (x atm)(0.34g/L)
x = 1.45 atm
The pressure of the water is 1.45 atm. (The other 0.90 atm is due to air pressure.
4)How can you make a saturated solution from an supersaturated solution?
Add a seed crystal – the solute will crystallize out until you get a saturated solution.
5)How can you make a supersaturated solution from a saturated solution?
If it’s a hot saturated solution, you can cool it. If it’s not, you can let the solvent evaporate to make it more concentrated.
6)How can you make an unsaturated solution from a saturated solution?
Add solvent.
7)What is the molarity of a solution made when you dilute 35 grams of sodium carbonate to a volume of 3,400 mL?
0.097 M
8)Explain how you would make 450 mL of a 0.25 M calcium chloride solution.
Add water to 12.5 grams of calcium chloride until the solution has a final volume of 450 mL.
Molarity Practice Worksheet
Find the molarity of the following solutions:
1)0.5 moles of sodium chloride is dissolved to make 0.05 liters of solution.
2)0.5 grams of sodium chloride is dissolved to make 0.05 liters of solution.
3)0.5 grams of sodium chloride is dissolved to make 0.05 mL of solution.
4)734 grams of lithium sulfate are dissolved to make 2500 mL of solution.
5)6.7 x 10-2 grams of Pb(C2H3O2)4 are dissolved to make 3.5 mL of solution.
6)I have two solutions. In the first solution, 1.0 moles of sodium chloride is dissolved to make 1.0 liters of solution. In the second one, 1.0 moles of sodium chloride is added to 1.0 liters of water. Is the molarity of each solution the same? Explain your answer.
Solutions to the Molarity Practice Worksheet
For the first five problems, you need to use the equation that says that the molarity of a solution is equal to the number of moles of solute divided by the number of liters of solution.
1)In this problem, simply solve using the molarity equation to find that the concentration of the solution is 10 M.
2)To use the molarity equation, you need to convert grams of sodium chloride to moles of sodium chloride before you can use the molarity equation. Because you have 0.0085 moles of NaCl in this solution, the total concentration is 0.17 M.
3)To use the molarity equation, you need to convert grams of NaCl to moles and mL of solution to liters. When you do this, the total concentration of the solution is 170.9 M. As it turns out, this isn’t a realistic value for molarity, so you’d never see a solution with this concentration out in the real world. Why did I give it to you then? I did it because I wanted you to see that just by changing a few units, you can get very different final answers.
4)This is done in the same method that you’d solve #3. Because you have 6.68 moles of Li2SO4 and 2.500 liters of water, the overall molarity of your solution is 2.67 M.
5)This problem is also solved in the same way as #3 and #4. Because you have 1.51 x 10-4 moles of Pb(C2H3O2)4, and 0.0035 L of water, the total concentration is 4.32 x 10-2 M, or 0.0432 M.
6)The equation for molarity states that the molarity of a solution is equal to the number of moles of solute divided by the number of liters of solution. In the first equation, the molarity will clearly be equal to 1.0 M, because there are 1.0 moles of NaCl and a solution volume of 1.0 L. In the second solution, the molarity will be different, because the solution volume will be greater than 1.0 liters. Why? If you already have 1.0 L of water and add 1.0 moles of salt to it, it will overflow, right? This is because the volume will be (roughly) equal to the volume of the water plus the volume of the salt, which will be greater than 1.0 L. It is for this reason that when you make a solution, you always dissolve the solute in only a little bit of water and then add water to make your final volume.