You purchase a bottle of concentrated sulfuric acid from a chemical supplier. The bottle reads Sulfuric acid (95% w/w) plastic coated safety bottle. The label lists the density of the acid as 1.85 g/mL and the molar mass as 98.08 g/mol, but the label fails to list the molarity of the concentrated acid! Calculate the molarity of the sulfuric acid based upon the information given.

The molarity of the sulfuric acid is 0.018 M

Explanation:

The molarity of a solution is the number of moles of the solute (sulfuric acid in this case) in a 1-liter solution.

Every 100 g of the solution, we have 95 g sulfuric acid because its concentration is 95% w/w.

With the density, we can calculate how many liters are 100 g of solution:

density = mass / volume

1.85 g / ml = 100 g / volume

volume = 100 g / 1.85 g/ml

volume = 54.1 ml or 0.0541 l

Now, we know that we have 95 g sulfuric acid in 0.0541 l solution. In 1 l, we have then:

1 l * 95g / 0.0541 l = 1.756 g sulfuric acid.

But we want to know how many moles sulfuric acid we have per liter. Then, using the molar mass, we can calculate how many moles there are in 1.756 g sulfuric acid:

1.756 g * 1 mol / 98.08 g = 0.018 mol

The molarity is 0.018 M