Concentration Calculations: Problems and solutions in Molarity

Molarity

The most common unit of concentration in chemistry is molarity, defined as the number of moles of solute dissolved per liter (or cubic decimeter) of solution. It can also be defined as the number of millimoles of solute per milliliter of solution. The symbol for molarity is an italic capital M; it s unit is molar, symbolized M. (Some books use Mfor both.) Do not use lowercase letters for either! We use mol as an abbreviation for mole; we do not use either capitalMor lowercase m. We must be sure to understand the difference between concentration and quantity of solute.

Problem 1 A cup labeled A has two lumps of sugar in it and is filled with tea. A cup labeled B has one lump of sugar, and is half filled. 

(a) Which cup, if either, has more sugar in it? 

(b) In which cup, if either, is the tea sweeter?

Solution 
(a) Cup A has more sugar. (Two lumps is more than one.)
(b) The tea is equally sweet in each, because the concentration of sugar is the same in each.
Be sure to note in each chemistry problem the difference between quantity of solute and concentration of solute!

Problem2:

If 2.00 L of solution contains 4.50 mol of solute, what is the molarity of the solution?

Problem 3
Show that a solution containing 4.50 mmol of solute in 2.00 mL of solution is also 2.25 M.

Because molarity is a ratio, it can be used as a factor in solving problems. Wherever the symbol M appears, it can be replaced by mol/L or mmol/mL, and for 1/M, their reciprocals can be substituted.

Problem 4 

Calculate the number of moles of solute contained in 3.00 L of 4.00 M solution.

Problem 5

Calculate the volume of a 2.80 M solution that contains 4.00 mol of solute.

If a solution is diluted with solvent, its number of moles of solute does not change, but its molarity gets lower.