Understanding Molarity and Molality: A Practical Example with Sodium Hydroxide

In this article, we will explore the concepts of molarity and molality, and apply these concepts to a specific example involving sodium hydroxide (NaOH). We will calculate the molarity of a solution when 20 grams of NaOH is dissolved in 500 milliliters of water. By the end of this article, you will have a clear understanding of how to calculate both molarity and molality, and the difference between the two.

What is Molarity?

Molarity is defined as the number of moles of solute per liter of solution. The formula for molarity (M) is:

M n / V [/math]

where n is the number of moles of solute and V is the volume of the solution in liters.

Calculating Molarity

Let's begin by calculating the moles of NaOH. Given that the molar mass of NaOH is approximately 40 grams per mole, we can calculate the number of moles as follows:

n m / M where m m NaOH 20.0 g , M M NaOH 40.0 g ?1mol mol?1 n 20.0 g / 40.0 g ?1mol 0.5 mol [/math>

Next, we need the volume of the solution in liters. Since the solution volume is 500 milliliters (0.5 liters), the molarity can be calculated as:

M n NaOH / V solution 0.5 mol / 0.5 L 1.00 mol ?1L

Therefore, the molarity of the solution is 1.00 mol/L.

What is Molality?

Molality, on the other hand, is defined as the number of moles of solute per kilogram of solvent. The formula for molality (m) is:

m n solute / m solvent

where nsolute is the number of moles of solute and m solvent is the mass of the solvent in kilograms.

Calculating Molality

To calculate molality, we need the mass of the solvent (water) in kilograms. Given that the density of water is approximately 1 g/mL, the mass of the solvent can be calculated as:

m solvent m water density 500 g ?1m L ?1 C m ?3 KM ?1 g ?1 m L ?3 m solute 0.5 kg [/math> m n solute / 0.5 kg 0.5 mol / 0.5 kg 1.00 mol ?1kg

Therefore, the molality of the solution is 1.00 mol/kg.

Key Differences Between Molarity and Molality

While molarity is dependent on the volume of the solution, molality is dependent on the mass of the solvent. As a result, changes in temperature or pressure (which can affect the volume of the solution) do not affect molality, whereas they can impact molarity.

Closing Remarks

In summary, we have demonstrated how to calculate both molarity and molality using a practical example with sodium hydroxide (NaOH). By understanding the difference between these measures of concentration, you can better apply these concepts in your own chemical calculations and experiments.