Question

The percentage of sulphur in an organic compound whose amount of \(0.32\) g produces \(0.233 \mathrm{~g}\) of \(\mathrm{BaSO}_{4}\) (Atomic weight of \(\mathrm{Ba}=137, \mathrm{~S}=32\) ) is: (a) \(1.0\) (b) \(10.0\) (c) \(25.3\) (d) \(32.1\)

Short answer

The percentage of sulphur is 10.0%.

Step-by-step solution

Determine Relevant Molecular Weights

First, we need to find the molar mass of \( \text{BaSO}_4 \). The atomic weights are: \( \text{Ba} = 137 \), \( \text{S} = 32 \), and \( \text{O} = 16 \). Since there are four oxygen atoms, the molar mass is calculated as follows: \[ \text{Molar mass of } \text{BaSO}_4 = 137 + 32 + 4 \times 16 = 233 \text{ g/mol} \]

Calculate Moles of BaSO4

Using the mass of \( \text{BaSO}_4 \) produced, we calculate the moles of \( \text{BaSO}_4 \) using its molar mass: \[ \text{Moles of BaSO}_4 = \frac{0.233 \text{ g}}{233 \text{ g/mol}} \approx 0.001 \text{ mol} \]

Determine Moles of Sulphur

One mole of \( \text{BaSO}_4 \) contains one mole of sulphur. Therefore, the moles of sulphur are the same as that of \( \text{BaSO}_4 \): \[ \text{Moles of S} = 0.001 \text{ mol} \]

Calculate Mass of Sulphur

Now, to find the mass of sulphur, use its atomic weight: \[ \text{Mass of S} = 0.001 \text{ mol} \times 32 \text{ g/mol} = 0.032 \text{ g} \]

Calculate Percentage of Sulphur

Finally, calculate the percentage of sulphur in the original compound: \[ \text{Percentage of S} = \left(\frac{0.032 \text{ g}}{0.32 \text{ g}}\right) \times 100\% = 10\% \]

Key concepts

Percentage Composition in Organic Chemistry

Percentage composition is a fundamental concept in chemistry that tells us what proportion of each element is present in a compound, relative to the entire mass. In organic chemistry, finding the percentage composition, especially of elements like sulfur, helps us understand the makeup of the compound better. Knowing the percentage composition provides valuable insight into the compound's chemical structure and properties.

To calculate the percentage composition, you need to know the mass of the element in a certain amount of the compound as well as the total mass of the compound. The formula is:

• \( \text{Percentage of Element} = \left( \frac{\text{Mass of Element in the Compound}}{\text{Total Mass of Compound}} \right) \times 100\% \)

In our exercise, we determined that the percentage of sulfur is calculated from the mass of sulfur derived from the mass of \( \text{BaSO}_4 \) produced by the compound. By understanding percentage composition, chemists can identify how compounds react with others and predict possible transformations in metabolic processes in organic chemistry.

Stoichiometry in Chemistry Calculations

Stoichiometry is the big brother of chemical calculations. It allows chemists to convert between masses, moles, and volumes of reactants and products in a chemical reaction. By using stoichiometry, we can solve for unknown quantities if we know other quantities.

The key to mastering stoichiometry is understanding the mole concept, where one mole contains \(6.022 \times 10^{23}\) entities (such as atoms or molecules). This is foundational for calculating the ratios between reactants and products.

In our solution, we needed to calculate moles of \( \text{BaSO}_4 \) from its mass to eventually find the moles of sulfur. We achieved this by dividing the mass of \( \text{BaSO}_4 \) (0.233 g) by its molar mass (233 g/mol). Thus:

• \( \text{Moles of BaSO}_4 = \frac{0.233 \text{ g}}{233 \text{ g/mol}} \approx 0.001 \text{ mol} \)
• \( \text{Moles of S} = 0.001 \text{ mol} \)

These calculations reiterate the concept of mole ratios and how stoichiometry directly connects to various chemical transformations. It is a powerful tool that is essential for quantitative aspects in chemistry.

Determining Molecular Weight

Molecular weight, or molar mass, is crucial for understanding how much one mole of a compound weighs. It's especially useful in organic chemistry for preparing solutions of known concentrations and in calculations involving reaction stoichiometry.

To find the molecular weight, you sum up the atomic weights of all atoms in a molecule. In this exercise, we determined the molecular weight of \( \text{BaSO}_4 \), a key step to calculate how much sulfur was in that mass:

• Atomic weights used: \( \text{Ba} = 137 \), \( \text{S} = 32 \), \( \text{O} = 16 \)
• Calculated Molecular Weight of \( \text{BaSO}_4 = 137 + 32 + 4 \times 16 = 233 \text{ g/mol} \)

The knowledge of molecular weight helps quantify reactions and ensure accurate chemical reactions. It is fundamental across many fields beyond organic chemistry, aiding in research, pharmaceuticals, and materials science.