Question

Maximum number of molecules will be in: (a) \(1 \mathrm{~g}\) of \(\mathrm{H}_{2}\) (b) \(10 \mathrm{~g}\) of \(\mathrm{H}_{2}\) (c) \(22 \mathrm{~g}\) of \(\mathrm{O}_{2}\) (d) \(44 \mathrm{~g}\) of \(\mathrm{CO}_{2}\)

Short answer

10 g of H₂ has the maximum number of molecules.

Step-by-step solution

Calculate Moles of H₂

First, determine the molecular weight of \(\mathrm{H}_{2}\), which is \(2 \) grams/mole. Then calculate the moles of \(\mathrm{H}_{2}\) in 1 gram and 10 grams:- For 1g of \(\mathrm{H}_{2}\), moles = \(\frac{1}{2} = 0.5\).- For 10g of \(\mathrm{H}_{2}\), moles = \(\frac{10}{2} = 5\).Thus, the moles of \(\mathrm{H}_{2}\) in 1g is 0.5 and in 10g is 5.

Calculate Moles of Other Gases

Now find the moles of \(\mathrm{O}_{2}\) and \(\mathrm{CO}_{2}\):- Molecular weight of \(\mathrm{O}_{2}\) = 32 grams/mole. \(22g\) of \(\mathrm{O}_{2}\): moles = \(\frac{22}{32} \approx 0.6875\).- Molecular weight of \(\mathrm{CO}_{2}\) = 44 grams/mole. \(44g\) of \(\mathrm{CO}_{2}\): moles = \(\frac{44}{44} = 1\).Thus, there are approximately 0.6875 moles of \(\mathrm{O}_{2}\) and 1 mole of \(\mathrm{CO}_{2}\).

Compare Moles to Find Maximum

Compare the moles of each substance to determine which has the most:- \(0.5\) moles in \(1g\ \mathrm{H}_{2}\).- \(5\) moles in \(10g\ \mathrm{H}_{2}\).- Approximately \(0.6875\) moles in \(22g\ \mathrm{O}_{2}\).- \(1\) mole in \(44g\ \mathrm{CO}_{2}\).10g of \(\mathrm{H}_{2}\) contains the most moles, which means it has the maximum number of molecules.

Key concepts

Molecule Counting

Molecule counting is crucial when dealing with chemical calculations, particularly when comparing different substances by the number of particles they contain. Each molecule is made of atoms bonded together in a specific arrangement, and counting them helps us understand chemical quantities at the molecular level.
The essence of molecule counting lies in utilizing Avogadro’s number, which has a value of \(6.022 \times 10^{23}\) molecules per mole. This number allows us to convert between moles, which are a measure of quantity, and the raw number of molecules present. For example, if a compound has 1 mole, it contains exactly \(6.022 \times 10^{23}\) molecules.
Counting the molecules lets us calculate and understand chemical reactions better because the reaction equation often defines the number of molecules that react with each other.

Molar Mass

The molar mass of a substance is what you need to think of as the weight of one mole of that substance. It’s the sum of the atomic masses of all the elements in a molecule, measured in grams per mole.

• For instance, hydrogen, represented as \(H_2\), has a molar mass of \(2\) grams/mole since it consists of two hydrogen atoms, each weighing about \(1\) gram/mole.


• Oxygen, \(O_2\), has a molar mass of \(32\) grams/mole because each oxygen atom weighs approximately \(16\) grams/mole.


• Carbon dioxide, \(CO_2\), is a bit more complex. It combines the weights of carbon (\(12\) grams/mole) plus twice the weight of oxygen (\(2 \times 16\) grams/mole), resulting in a molar mass of \(44\) grams/mole.

Understanding molar mass is essential for relating the mass of a material in grams to the number of molecules, via moles.

Conversion of Mass to Moles

To engage in chemical calculations, it's vital to convert between mass and moles, enabling a deeper comprehension of the reaction's extent. The conversion relies on the formula:\[ \text{Moles} = \frac{\text{Mass in grams}}{\text{Molar mass in grams/mole}} \]Let’s walk through an example: If you have \(10\) grams of \(H_2\), you would divide \(10\) by the \(2\) grams/mole molar mass, resulting in \(5\) moles.
Similarly, to determine how many moles are in \(22\) grams of \(O_2\), divide \(22\) by \(32\), which equals approximately \(0.6875\) moles.
This method is foundational for comparing quantities of different chemical substances on an atomic level, as moles provide a consistent measure for joining masses across different substances.

Comparing Moles

Comparing moles is a critical part of chemical calculations, as it enables you to determine which substance contains more molecules. Following the conversion of mass to moles, these values can be directly compared.
More moles mean more molecules, and thus, if you have \(5\) moles of \(H_2\) versus \(1\) mole of \(CO_2\), \(H_2\) evidently has more molecules corresponding to its mole ratio.
In our example, \(10\) grams of \(H_2\) yielded \(5\) moles, while \(44\) grams of \(CO_2\) were \(1\) mole. Clearly, \(H_2\) outweighs in quantity when you look at the molecular level.
Comparing the mole values, therefore, lets you determine which sample has the larger number of molecules, providing insights into chemical density and potential reaction outcomes.