Comprehensive Study Notes on Stoichiometry: Molar Mass and Molecular Calculations

General Course Information and Stoichiometry Fundamentals

The study materials correspond to the date of March 13, 2026, marking the third partial assessment session. The session is identified with the instruction or oversight of Clemente and involves specific grading or participation criteria including 5 seals and 19 hits or correct answers. The core subject matter of these notes is Stoichiometry (Estequiometría).

Molar mass ($M$) is defined as the algebraic sum of the atomic masses of the elements that conform or compose a chemical formula, typically expressed in units of grams per mole ($g/mol$). Essential constants for these calculations include the relationship of $1\,\text{mol}$ to Avogadro's number, defined here as $6.023 \times 10^{23}$ molecules. Additionally, in terms of volume for substances in a gaseous state under standard conditions, $1\,\text{mol}$ is equivalent to $22.4\,\text{L}$.

Detailed Calculation of Molar Masses for Various Compounds

To determine the molar mass of a compound, the atomic mass of each constituent element is multiplied by the number of atoms of that element present in the formula. For Water ($H_2O$), the calculation involves Hydrogen ($H: 2 \times 1\,\text{mol} = 2\,\text{mol}$) and Oxygen ($O: 1 \times 16\,\text{mol} = 16\,\text{mol}$), resulting in a total molar mass of $18\,\text{mol}$. For Sulfuric Acid ($H_2SO_4$), the components are Hydrogen ($H: 2 \times 1\,\text{mol} = 2\,\text{mol}$), Sulfur ($S: 1 \times 32\,\text{mol} = 32\,\text{mol}$), and Oxygen ($O: 4 \times 16\,\text{mol} = 64\,\text{mol}$), summing to a total of $98\,\text{mol}$.

Similar calculations are performed for other substances. Hydrochloric Acid ($HCl$), referred to in the text as "Acido clorilico," consists of Hydrogen ($H: 1 \times 1\,\text{mol} = 1\,\text{mol}$) and Chlorine ($Cl: 1 \times 35\,\text{mol} = 35\,\text{mol}$), totaling $36\,\text{mol}$. Calcium Carbonate ($CaCO_3$), or "Carbonato de calcio," includes Calcium ($Ca: 1 \times 40\,\text{mol} = 40\,\text{mol}$), Carbon ($C: 1 \times 12\,\text{mol} = 12\,\text{mol}$), and Oxygen ($O: 3 \times 16\,\text{mol} = 48\,\text{mol}$), yielding a total of $100\,\text{mol}$.

Aluminum Sulfite ($Al_2(SO_3)_3$), or "sulfito de aluminio," yields a molar mass through Aluminum ($Al: 2 \times 27\,\text{mol} = 54\,\text{mol}$), Sulfur ($S: 3 \times 32\,\text{mol} = 96\,\text{mol}$), and Oxygen ($O: 9 \times 16\,\text{mol} = 144\,\text{mol}$). These sums result in a compound mass of $294\,\text{g/mol}$, which is noted to be equivalent to $6.023 \times 10^{23}$ molecules. Nitric Acid ($HNO_3$) is calculated with Hydrogen ($H: 1 \times 1\,\text{mol} = 1\,\text{mol}$), Nitrogen ($N: 1 \times 14\,\text{mol} = 14\,\text{mol}$), and Oxygen ($O: 3 \times 16\,\text{mol} = 48\,\text{mol}$), totaling $63\,\text{g/mol}$. Finally, Ammonium Sulfide ($(NH_4)_2S$), or "sulfuro de amonio," consists of Nitrogen ($N: 2 \times 14\,\text{mol} = 28\,\text{mol}$), Hydrogen ($H: 8 \times 1\,\text{mol} = 8\,\text{mol}$), and Sulfur ($S: 1 \times 32\,\text{mol} = 32\,\text{mol}$), summing to a total mass of $68\,\text{g/mol}$.

Practical Application: Quantitative Analysis of Water ($H_2O$)

In a hypothetical scenario where there are $27\,\text{g}$ of water ($H_2O$), several quantitative properties can be derived. First, the number of moles is calculated by dividing the given mass by the molar mass ($18\,\text{g/mol}$). Since $1\,\text{mol} = 18\,\text{g}$, then $27\,\text{g}$ is equivalent to $1.5\,\text{moles}$. To find the number of molecules of water, the result is multiplied by Avogadro's number ($1.5 \times 6.023 \times 10^{23}$), which results in $9.0345 \times 10^{23}$ molecules.

To determine the number of Hydrogen atoms within this sample, the molecular count is multiplied by the number of Hydrogen atoms in the formula (2), resulting in $1.8069 \times 10^{24}$ atoms of Hydrogen. In terms of mass, since $1\,\text{mol}$ of water contains $2\,\text{g}$ of Hydrogen, $1.5\,\text{moles}$ contains $3\,\text{g}$ of Hydrogen. Furthermore, if the water were in a gaseous state under normal conditions, the volume occupied would be calculated by multiplying the moles by the molar volume ($1.5 \times 22.4\,\text{L}$), resulting in $33.6\,\text{L}$ (notated in the transcript as $33.64\,\text{L}$).

Practical Application: Quantitative Analysis of Sulfuric Acid ($H_2SO_4$)

Given a sample of $196\,\text{g}$ of Sulfuric Acid ($H_2SO_4$), multiple metrics are calculated based on its molar mass of $98\,\text{g/mol}$. The number of moles in the molecule is determined to be $2\,\text{moles}$ ($196\,\text{g} / 98\,\text{g/mol}$). Consequently, the total number of molecules in the sample is $1.2046 \times 10^{24}$, calculated as $2 \times 6.023 \times 10^{23}$.

The atomic composition of the sample is further broken down as follows: the number of Hydrogen atoms is $2.4092 \times 10^{24}$ ($2 \times 1.2046 \times 10^{24}$), the number of Sulfur atoms is $1.2046 \times 10^{24}$, and the number of Oxygen atoms is $4.8184 \times 10^{24}$ ($4 \times 1.2046 \times 10^{24}$).

Regarding the mass of individual elements within the $196\,\text{g}$ sample, there are $4\,\text{g}$ of Hydrogen ($2\,\text{moles} \times 2\,\text{g/mol}$), $64\,\text{g}$ of Sulfur ($2\,\text{moles} \times 32\,\text{g/mol}$), and $128\,\text{g}$ of Oxygen ($2\,\text{moles} \times 64\,\text{g/mol}$). Finally, if the acid were in a gaseous form under standard conditions, it would occupy a volume of $44.8\,\text{L}$, derived from the calculation $2\,\text{moles} \times 22.4\,\text{L/mol}$.