Molarity , molality and normality formula and their calculation

### Molarity, Molality, and Normality: Understanding Concentration Units

In chemistry, concentration is an essential concept that quantifies the amount of solute present in a given amount of solvent or solution. The concentration of a solution can be expressed in several ways, including **molarity**, **molality**, and **normality**. Each of these units of concentration has its specific uses depending on the context of the chemical reactions or processes being studied. Understanding the differences between these units is crucial for accurate calculations in laboratory experiments and industrial applications.

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### 1. **Molarity (M)**

Molarity is one of the most commonly used units of concentration in chemistry. It represents the number of moles of solute dissolved in one liter of solution. It is often used in reactions that take place in aqueous solutions, particularly in titrations and other analytical methods.

#### Definition of Molarity:
- **Molarity (M)** is defined as the number of moles of solute per liter of solution.

\[
M = \frac{\text{moles of solute}}{\text{liters of solution}}
\]

#### Formula for Molarity:
\[
M = \frac{n_{\text{solute}}}{V_{\text{solution}}}
\]
Where:
- \( n_{\text{solute}} \) = number of moles of solute
- \( V_{\text{solution}} \) = volume of solution in liters (L)

#### Example:
If 1 mole of NaCl (sodium chloride) is dissolved in 1 liter of water, the molarity of the solution would be:
\[
M = \frac{1 \, \text{mol}}{1 \, \text{L}} = 1 \, \text{M}
\]
This means the solution has a concentration of 1 mole of NaCl per liter.

#### Units:
The unit of molarity is **moles per liter (mol/L)** or simply **M**.

#### Molarity vs. Molality:
While molarity is used for solutions where the volume is the primary focus (e.g., aqueous solutions), it can be temperature-dependent because volume changes with temperature. This makes molarity less reliable when dealing with solutions at varying temperatures.

2. **Molality (m)**

Molality is another concentration unit that measures the number of moles of solute per kilogram of solvent. Unlike molarity, molality is temperature-independent because mass does not change with temperature. This makes molality particularly useful in scenarios where temperature fluctuations are significant.

Definition of Molality:
- **Molality (m)** is defined as the number of moles of solute per kilogram of solvent.

\[
m = \frac{\text{moles of solute}}{\text{kilograms of solvent}}
\]

#### Formula for Molality:
\[
m = \frac{n_{\text{solute}}}{m_{\text{solvent}}}
\]
Where:
- \( n_{\text{solute}} \) = number of moles of solute
- \( m_{\text{solvent}} \) = mass of solvent in kilograms (kg)

#### Example:
If 1 mole of NaCl is dissolved in 1 kilogram of water, the molality of the solution would be:
\[
m = \frac{1 \, \text{mol}}{1 \, \text{kg}} = 1 \, \text{mol/kg}
\]
This means the solution has a concentration of 1 mole of NaCl per kilogram of water.

1. NME chemistry By: R.Vaishnavi II Msc Mathematics

2. Problems Molarity : 1. What is the molarity of a 250 ml solution containing 0.35 moles N acl ? Soln : first we convert ml to l, 250ml(1L/1000ml) = 0.25L Formula: M = Molarity = Moles of soute Litres of solution

3. 0.35 mole Nacl ̿ 0.25 L solution = 1.4 M Nacl 2. Suppose we have 35 ml of a 0.85M Mgcl 2 solution. How many moles of Mgcl 2 are present in the solution? soln : first we convert ml to l 35ml(1L/1000ml) = 0.035L Using t he formula of molarity , M = Molarity Moles of solute ̿ Literes of solution Mole of solute = Molarity * Literes of solution

4. = (0.035L)*(0.85mole) = 0.030 mol Mgcl 2 B . Molality : 1. Calculate the molality ofan antifreeze solution made by dissolving 186g of antifreeze (c 2 H 6 O 2 ) in 2Kgofwater? soln : first we convert grams to moles, =186g c 2 H 6 O 2 /62.07g c 2 H 6 O 2 = 2.99 = 3 mol c 2 H 6 O 2

5. m = Molality Moles of solute ̿ Kg of solvent m = 3 mole/2Kg = 2 m c 2 H 6 O 2 2. What is the molality of a solution in which 2.75 moles of Nacl are dissolved in 1.25Kg of water? soln : Given, moles of solute = 2.75 mole Nacl mass of solvent = 1.25 Kg water To find,Molality (m) of solution, m = Molality Moles of solute ̿ Kg of solvent

6. = (2.75 mole Nacl )/(1.25 of water) = 2.2 m Nacl C. Normality: 1.Find the normality of H 2 So 4 having 49g H 2 So 4 present in 500ml of solution? soln : first we convert ml to L, 500ml = (500/1000)L = ½ L Using the normality formula, N = Normality = ( Equaivalent of solute)/( litere of solution)

7. = 49g/(92/2)*(500/1000L) = 49g/46*(1/2)L = 2.13 N 2. Calculate the normality of NaoH having 2g is present in 800ml solution? soln : first we convert ml to L, 800ml = (800/1000L) = (8/10)L N= 2g/(40/1)*(0.8) = 0.06 N

8. D. Mass percentage: 1. If 28.5g of calcium hydroxide Ca(OH) 2 is dissolved in enough to make 185g of solution, What is the percent by mass of Ca(OH) 2 in the solution? soln : Given, Mass of solute = 28.5g, Mass of solution = 185g Mass% = (Mass of solute/Mass of solution)*100 = (28.5g/185g)*100 = 15.4%

9. 2. What is the mass % of Na 2 so 4 in a solution made by dissolving 25.g Na 2 so 4 in 225.0g H 2 O? soln : Given, Mass of solute = 25.0g Na 2 so 4 Mass of solvent = 225.0 H 2 O Using the Mass% formula, Mass% = (25.0g Na 2 so 4 )/(225.0gH 2 O+25.0 Na 2 so 4 )

10. = 25.0/250.0 = 10% E. Volume percentage: 1. A solution is made from 35ml of methanol and 65ml of water. Calculate the volume percentage? soln : Given, Volume of methanol = 35ml Volume of water(solvent) = 65ml Using the volume percentage, = ((Volume of the solute/Volume of the solution)*100

11. =[Volume of the solute/(Volume of the solute+Volume of the solvent)]*100 = [35/(35+65)]*100 = (35/100)*100 = 35% 2. Calculate the volume of ethanol in 200ml solution of 20% v/v aqueous solution of ethanol? soln : Given, Volume of aqueous solution = 200ml Volume% = 20% Using the formula of volume percentage, 20 = [Volume of ethanol(solute)/200]*100 Volume o f ethanol = (20*200)/100 = 40ml

12. F. Mole Fraction: 1. Calculate the mole fraction of Mgcl 2 and H 2 O, if 2 moles of Mgcl 2 are dissolved in 100 grams of water? soln : Given, the number of mole of MgCl 2 = A = 2 mole The molecular weight of H 2 O = 18 gram per mole Number of moles of H 2 O = B = (Given weight/Molecular weight) B = 55.6 moles Using the mole fraction formula, Mole fraction of MgCl 2 = Number of moles of MgCl 2 /Total moles = A/(A+B) = 2/57.5 = 0.034

13. Mole fraction of H 2 O = B/(A+B) = 55.6/57.6 = 0.96 2. Calculate the mole fraction of Ethanol and water, if 3 moles of ethanol are dissolved in 1000 grams of water? Soln : The molecular weight of H 2 O = 18 gram per mole Number of moles of H 2 O = A = Given weight /Molecular weight = 55.6 moles Number of moles of ethanol = B = 3 moles Moles fraction of ethanol = B/(A+B) = 3/58.6 = 0.05119

14. Mole fraction of H 2 O = A/(A+B) = 55.6/58.6 = 0.9488

15. Thank you