Molar Concentration Formula

Solution and its related computation are very important in science. Calculating the molar concentration of a solution is a comparatively straightforward process. We will determine how many moles of a substance we have and then divide it by the volume of the solution. In this topic, we will discuss the formula for the Molar Concentration formula with examples. Let us learn the concept!

                                                                                                                                        Source:  en.wikipedia.org

Molar Concentration Formula

Definition of Molar Concentration

Molar concentration is the most convenient method of expressing the concentration of a solute in the given solution. Molarity is the number of moles of the solute dissolved per liter of the solution. Thus M = mol per L. All mole calculations will determine the amount in moles of the solution, for which it is the molar concentration.

The balanced chemical equation always leads to a mole ratio between the acid and the base. It, in turn, leads to the number of moles of the base. We can compute the molar concentration by dividing the number of moles by the volume of the solution.

Formula

\(Molar Concentration = \frac{Amount\;in\;moles}{Volume\;of\;solution}\)

An early step to determine the molar concentration is finding the mass of the solute which is the grams of the dissolved substance. Problems usually state the mass, although we may have to convert to grams from some other unit.

Also, to find the number of moles of a solute, we first need to calculate the molar mass of the substance. For the chemical formula for the solute, we have to use the atomic mass of the elements. For any element that appears repeatedly, we have to multiply the mass by the number of atoms per molecule of that element.

Say, for example, Acetic acid is \(CH_3COOH\). Here, the molecule has a total of two carbon atoms, two oxygen atoms, and four hydrogen atoms. We will multiply the atomic mass of carbon by 2, oxygen by 2 and hydrogen by 4 and then add the results to get the total molar mass in grams per mole.

Since the atomic masses of carbon, oxygen and hydrogen are 12.01, 16.00 and 1.008, respectively. After multiplying the masses and number of quantities we get

\((12.01 \times 2) + (16.00 \times 2) + (1.008 \times 4)\)

= 60.05 grams per mole.

Now, to calculate the moles of the solute, we will divide the mass in grams by grams per mole. For example, we have 10g of acetic acid. Then by dividing 10g by 60.05 g per mole will give 0.1665 moles of solute.

To calculate the Molar Concentration, we will find the molar concentration by dividing the moles by liters of water used in the solution. For example, the acetic acid here is completely dissolved in 1.25 L of water. Then divide 0.1665 moles by 1.25 L to get the molar concentration, which will be 0.1332 M.

Solved Examples

Q.1: Determine the molar concentration of NaOH, due to the reaction between HCl and NaOH.

Solution:

The balanced chemical equation is given as,

\(HCl + NaOH → NaCl + H_2O\)

For an acid

\(n(HCl) = \frac{35.0}{ 1000 }dm^3 \times 0.250 mol dm^{-3}\)

= \(8.75 \times 10^{-3} mol\)

The mole ratio here is 1 :1.

\(The amount of NaOH present is = 8.75 \times 10^{-3} mol\).

Volume of aqueous NaOH,

\(25 cm^3 = \frac{25}{1000} dm^3\)

= \(25 × 10ˆ{-3} dm^3\)

Now we have the formula:

Molar Concentration = \(\frac{Amount\;in\;moles}{Volume\;of\;solution}\)

Molar Concentration =\( \frac{8.75 \times 10^{-3} mol}{25 × 10ˆ{-3} dm^3}\)

Molar concentration of NaOH = \(0.350 mol dm^{-3}\)