Question

Which has maximum number of molecules? (a) \(1.7 \mathrm{~g} \mathrm{NH}_{3}\) (b) \(2 \mathrm{~g} \mathrm{He}\) (c) \(4.6 \mathrm{~g} \mathrm{NO}_{2}\) (d) \(3.2 \mathrm{~g} \mathrm{SO}_{2}\)

Short answer

The helium (He) with 2 g has the highest number of molecules.

Step-by-step solution

Molar Mass Calculation

First, we need to calculate the molar mass of each compound. - For NH₃: - Molar mass = (1 * 14) + (3 * 1) = 17 g/mol - For He: - Molar mass = 4 g/mol (since it's a monoatomic gas) - For NO₂: - Molar mass = (1 * 14) + (2 * 16) = 46 g/mol - For SO₂: - Molar mass = (1 * 32) + (2 * 16) = 64 g/mol

Moles Calculation

Using the molar mass from Step 1, calculate the number of moles in each sample.- Moles of NH₃: \( \frac{1.7\, \text{g}}{17\, \text{g/mol}} = 0.1\, \text{moles} \)- Moles of He: \( \frac{2\, \text{g}}{4\, \text{g/mol}} = 0.5\, \text{moles} \)- Moles of NO₂: \( \frac{4.6\, \text{g}}{46\, \text{g/mol}} = 0.1\, \text{moles} \)- Moles of SO₂: \( \frac{3.2\, \text{g}}{64\, \text{g/mol}} = 0.05\, \text{moles} \)

Molecules Calculation

Determine the number of molecules by multiplying the moles by Avogadro's number (\(6.022 \times 10^{23}\, \text{molecules/mole}\)).- Molecules in NH₃: \( 0.1\, \text{moles} \times 6.022 \times 10^{23}\, \text{molecules/mole} = 6.022 \times 10^{22}\, \text{molecules} \)- Molecules in He: \( 0.5\, \text{moles} \times 6.022 \times 10^{23}\, \text{molecules/mole} = 3.011 \times 10^{23}\, \text{molecules} \)- Molecules in NO₂: \( 0.1\, \text{moles} \times 6.022 \times 10^{23}\, \text{molecules/mole} = 6.022 \times 10^{22}\, \text{molecules} \)- Molecules in SO₂: \( 0.05\, \text{moles} \times 6.022 \times 10^{23}\, \text{molecules/mole} = 3.011 \times 10^{22}\, \text{molecules} \)

Compare Molecules

Finally, compare the number of molecules calculated for each sample:- NH₃: \(6.022 \times 10^{22}\)- He: \(3.011 \times 10^{23}\)- NO₂: \(6.022 \times 10^{22}\)- SO₂: \(3.011 \times 10^{22}\)He has the maximum number of molecules.

Key concepts

Molar Mass

Molar mass is a term used in chemistry to define the mass of one mole of a chemical substance in grams. It's essentially the weight of 6.022 x 10^23 molecules (or atoms, for monoatomic substances) of that substance. To estimate the molar mass, you simply sum up the atomic masses of all the atoms in a molecule, as found on the periodic table.
For example, to find the molar mass of ammonia (23), you count the weight of nitrogen (14 g/mol) and add it to three hydrogens (1 g/mol each). That gives us a molar mass of 17 g/mol for 23.

• Nitrogen (23): 14 g/mol + 3(1 g/mol) = 17 g/mol
• Helium (f): 4 g/mol (since it's atomic and not a compound)
• Nitrogen dioxide (02): 14 g/mol + 2(16 g/mol) = 46 g/mol
• Sulfur dioxide (02): 32 g/mol + 2(16 g/mol) = 64 g/mol

Understanding molar mass is crucial because it serves as a bridge between the micro-world of atoms and molecules and the macroscopic world we interact with, enabling conversions between grams and moles, which is essential for calculations in chemistry.

Avogadro's Number

Avogadro's number, denoted as 6.022 x 10^23, is a fundamental constant in chemistry that represents the number of atoms or molecules contained in one mole of a substance. This number allows chemists to "count" particles at the molecular or atomic scale using the amount of substance in moles.
Think of it like a bridge that lets us translate between the incredibly small scale of individual molecules and the accessible, measurable scale we work with in laboratories. So, when you have 1 mole of water, you actually have 6.022 x 10^23 water molecules.

• It helps in expressing the large numbers naturally involved when talking about chemical amounts.
• Using Avogadro's number, you can convert between moles and molecules to make sense of chemical reactions and mass relationships.

This concept is essential to understand chemical equations and stoichiometry, as it is the key to navigating between the mass of substances (measured in grams) and the number of particles involved in chemical changes.

Chemical Molecules

Chemical molecules are formed when two or more atoms bond together chemically. This grouping of atoms serves as the building block of the universe, creating everything from the air we breathe to the complex sequences of flavors in a meal.
At an atomic level, a molecule is the smallest unit of a compound holding all the chemical properties of the compound. For instance, the ammonia molecule (23) is composed of one nitrogen atom bonded to three hydrogen atoms, displaying characteristics entirely different from individual nitrogen or hydrogen molecules.
When exploring chemical reactions, molecules undergo transformations where the bonds between atoms are broken and new bonds are formed, creating different molecules.
Understanding molecules helps in:

• Predicting the properties and behavior of substances.
• Balancing chemical equations, since reactions occur at the molecular level.
• Interpreting the roles substances play in broader physical scenarios, like metabolic processes or environmental chemistry.

Molecules are the fundamental components that drive the transformative power of chemistry, making the comprehension of their nature and behavior critical to mastering chemistry.