# How much of 8.00 mol/L sulphuric acid must you add to an empty 750. mL bottle to obtain a concentration of 1.50 mol/L?

Mar 30, 2017

If you wish to produce 750 mL of the 1.50 M solution, you will need 140.6 mL of the 8.00 M solution.

#### Explanation:

The key to solving this problem is to realize that the number of moles of ${H}_{2} S {O}_{4}$ that you will have in the 750 mL solution will be equal to the number of moles you must remove from the 8.00 M solution.

Since we know the desired concentration and volume (I assume we are to make a full 750 mL of the 1.50 M solution), we can use this to find the number of moles

$\frac{\text{moles" H_2SO_4 = 1.50 "mol}}{L} \times 0.750 L = 1.125$ mol

To find the volume of the concentrated solution needed, we start with the definition of molarity:

"molar concentration" = ("number of moles")/ ("volume in litres")

and rewrite it as

"volume in litres" = ("number of moles")/("molar concentration")

$\text{volume} = \frac{1.125}{8.00} = 0.1406 L$ or 140.6 mL

Place this in the bottle and top it up to 750 mL with water.

(Practical note: Put about 500 mL of water into the bottle first, then add the acid before topping it up. It is safer that way! )