Question

Two containers have equal weights of \(\mathrm{NO}_{2}\) and \(\mathrm{N}_{2} \mathrm{O} .\) The one containing more number of moles is (I) \(\mathrm{NO}_{2}\) (2) \(\mathrm{N}_{2} \mathrm{O}\) (3) both have same number of moles (4) cannot be determined

Short answer

The one containing more number of moles is (2) \(\text{N}_2\text{O}\).

Step-by-step solution

Understand Molar Mass

Calculate the molar masses of \(\text{NO}_2\) and \(\text{N}_2\text{O}\). Molar mass is found by adding the atomic masses of the atoms in the molecule. The atomic mass of nitrogen (\text{N}) is 14, and the atomic mass of oxygen (\text{O}) is 16.

Calculate Molar Mass of \(\text{NO}_2\)

For \(\text{NO}_2\): \(\text{Molar mass} = 14 + 2 \times 16 = 46\).

Calculate Molar Mass of \(\text{N}_2\text{O}\)

For \(\text{N}_2\text{O}\): \(\text{Molar mass} = 2 \times 14 + 16 = 44\).

Compare the Molar Masses

Since the weights of \(\text{NO}_2\) and \(\text{N}_2\text{O}\) are equal, determine which compound has more moles by comparing their molar masses. The compound with the lower molar mass will have more moles for the same total weight.

Determine the Number of Moles

Because \(\text{N}_2\text{O}\) has a lower molar mass (44) compared to \(\text{NO}_2\) (46), \(\text{N}_2\text{O}\) must have more moles since it takes fewer grams to make up one mole.

Key concepts

Molar Mass Calculation

The concept of molar mass is crucial in understanding chemical reactions and substance quantification. Molar mass is the mass of one mole of a given substance, typically measured in grams per mole (g/mol). To calculate the molar mass, sum the atomic masses of all the atoms in the molecule. For instance, consider \(\text{NO}_2\): The atomic mass of nitrogen (N) is 14, and the atomic mass of oxygen (O) is 16. Since \(\text{NO}_2\) contains one nitrogen atom and two oxygen atoms, its molar mass is calculated as follows:
\[ \text{Molar mass of NO}_2 = 14 + 2 \times 16 = 46 \].
Similarly, for \(\text{N}_2\text{O}\): With two nitrogen atoms and one oxygen atom, the calculation is:
\[ \text{Molar mass of N}_2\text{O} = 2 \times 14 + 16 = 44 \].
Knowing how to calculate the molar mass helps in many areas of chemistry, such as stoichiometry, where balancing chemical equations requires an understanding of the amounts of reactants and products.

Comparing Moles

Comparing moles is about understanding the number of particles (atoms, molecules, ions) present in a given mass of substance. One mole contains exactly \(6.022 \times 10^{23}\) entities, known as Avogadro's number. When two substances have equal mass, the number of moles in each substance can be different if their molar masses are different.
For example, let's compare \(\text{NO}_2\) and \(\text{N}_2\text{O}\). Despite having equal weights, the substance with the lower molar mass has more moles. We know:
\(\text{Molar mass of NO}_2 = 46 \)
\(\text{Molar mass of N}_2\text{O} = 44\)
Because \(\text{N}_2\text{O}\) has a lower molar mass, a given mass contains more moles of \(\text{N}_2\text{O}\) compared to \(\text{NO}_2\). This is because it takes fewer grams to make up one mole of \(\text{N}_2\text{O}\) than it does for \(\text{NO}_2\).

Atomic Masses

Understanding atomic masses is essential in chemistry as it forms the basis for calculating molar masses and comparing substances. Atomic mass (or atomic weight) is the mass of an individual atom, usually measured in atomic mass units (amu), where one amu is defined as one twelfth the mass of a carbon-12 atom. For example:

• Nitrogen (\text{N}) has an atomic mass of 14 amu
• Oxygen (\text{O}) has an atomic mass of 16 amu

These values are crucial when calculating the molar masses of compounds. For instance, the molecular formula for \(\text{NO}_2\) involves one nitrogen atom and two oxygen atoms. By adding the atomic masses, we get a molar mass of 46 g/mol. Similarly, \(\text{N}_2\text{O}\) has a molar mass determined by the sum of two nitrogen atoms and one oxygen atom, giving 44 g/mol. Atomic masses help predict and quantify how substances interact in chemical reactions, making it a key concept in both theoretical and practical chemistry.