Question

The number of oxalic acid molecules in \(100 \mathrm{ml}\) of \(0.02 \mathrm{~N}\) oxalic acid solution is: (a) \(6.023 \times 10^{22}\) (b) \(10^{-3}\) (c) \(6.022 \times 10^{20}\) (d) None of these

Short answer

The number of oxalic acid molecules is \(6.022 \times 10^{20}\). Option (c).

Step-by-step solution

Understanding Normality and Molarity

The normality ( ef{N}) of a solution refers to the gram equivalent per liter of solution. For oxalic acid, which dissociates to give two protons ( ef{2H^+}), the normality is twice the molarity. Therefore, the molarity ( ef{M}) is defined as ef{M = rac{N}{2}} given the equivalence factor of oxalic acid is 2.

Convert Normality to Molarity

Given that the normality ( ef{N}) of oxalic acid is ef{0.02 N}, we can calculate the molarity using the formula ef{M = rac{N}{2}}. Thus, ef{M = rac{0.02}{2} = 0.01} M. This means there are ef{0.01} moles of oxalic acid per liter.

Calculate Moles in 100 ml

Since molarity is moles per liter, and we have ef{0.01} M in ef{1000} ml, the moles in ef{100} ml is ef{0.01 imes rac{100}{1000} = 0.001} moles of oxalic acid.

Using Avogadro's Number to Find Molecules

To find the number of molecules, use Avogadro's number, which is approximately ef{6.022 imes 10^{23}} molecules/mole. Multiply the moles from the previous step: ef{0.001 ext{ moles} imes 6.022 imes 10^{23} ext{ molecules/mole} = 6.022 imes 10^{20}} molecules.

Key concepts

Normality and Molarity

Understanding the terms "normality" and "molarity" is crucial for solving problems related to solutions. Normality is a measure of concentration equivalent to the gram equivalent weight per liter. For solutions that involve reactions, normality takes into account the number of reactive units in the solute. For example, oxalic acid releases two protons when it dissociates, making its normality twice its molarity. Simply put, normality reflects how many moles of reactive units are in one liter of solution. So, given the normality of oxalic acid as \(0.02 \text{ N}\), we divide it by the equivalence factor (which is 2 for oxalic acid) to convert it into molarity. Thus, the formula for molarity becomes \( M = \frac{N}{2} = 0.01 \text{ M}\), helping us understand the number of solute molecules in a given volume.

Avogadro's Number

Avogadro's number is a fundamental constant in chemistry that connects the macroscopic world with the molecular level. It is defined as the number of particles, usually atoms or molecules, in one mole of a substance. This constant is approximately \(6.022 \times 10^{23}\) particles per mole. It is named after the Italian scientist Amedeo Avogadro, who contributed significantly to molecular theory. This number is immensely useful when converting moles of a substance to actual numbers of molecules or atoms. By using Avogadro's number, you translate the abstract notion of moles into something more tangible: the count of individual particles in a given amount of material. For instance, to find the number of molecules in a given amount of oxalic acid, you'd multiply the number of moles by Avogadro's number.

Moles Calculation

Calculating moles is an essential skill in chemistry that empowers you to connect solution concentrations to actual quantities of molecules. The mole concept bridges macroscopic measurements with the molecular scale. To calculate moles in a solution, you take into account the molarity, which denotes the number of moles per liter. For example, if the molarity of oxalic acid is \(0.01 \text{ M}\), this means you have \(0.01\) moles of oxalic acid in every liter of solution. If you need to find out how many moles are in a different volume, say \(100 \text{ ml}\) instead of \(1000 \text{ ml}\), you scale the moles proportionally: \(0.01 \times \frac{100}{1000} = 0.001\) moles. This calculation is useful for converting concentrations into specific amounts of substance, allowing you to use this data for further chemical calculations, like finding the number of molecules using Avogadro's number.