Question

A compound possess \(8 \%\) sulphur by mass. The least molecular mass is (a) 200 (b) 400 (c) 155 (d) 355

Short answer

The least molecular mass is 400 (answer b).

Step-by-step solution

Understanding the Problem

We need to find the least molecular mass of a compound that contains \(8\%\) sulfur by mass. This means that in every 100 grams of the compound, there are 8 grams of sulfur.

Setting Up the Equation

Let the least molecular mass of the compound be \(M\). Since \(8\%\) of \(M\) is the mass of the sulfur, we use the equation: \( \frac{8}{100} \times M = \text{mass of sulfur} \).

Finding the Molar Mass of Sulfur

The atomic mass of sulfur is \(32 \, \text{g/mol}\). In the least molecular formula, the compound should contain at least one sulfur atom.

Solving for the Least Molecular Mass

The minimum molecular mass \(M\) can be found by setting the mass of sulfur equal to \(32 \, \text{g/mol}\). Substituting into the equation: \[ \frac{8}{100} \times M = 32 \]

Calculating the Molecular Mass

Rearrange the equation to solve for \(M\): \[ M = \frac{32 \times 100}{8} \]Calculate: \[ M = 400 \]

Identifying the Correct Option

The least molecular mass of the compound is \(400\) grams/mol. Therefore, the correct answer is option (b) 400.

Key concepts

Sulfur Percentage

When we talk about the sulfur percentage in a compound, we are looking at how much sulfur is present relative to the total mass of the compound. To express this as a percentage, you calculate the mass of sulfur (from its atoms) that is found in a given mass of the compound and then convert it to a percentage.
In our specific problem, the compound contains 8% sulfur by mass. This means that for each 100 grams of the compound, 8 grams is sulfur. Understanding mass percentage is important because it helps in identifying how "rich" a compound is in a particular element, which can inform chemical applications and reactions.
Key points to remember:

• Mass percentage makes it easy to compare the composition of different compounds.
• Percentage composition provides insight into the possible identity of the compound or its reactivity.
• You can calculate percentage composition by comparing the mass of the element to the total mass and then multiplying by 100.

Least Molecular Mass

The least molecular mass of a compound refers to the smallest possible molecular weight that the compound can have while maintaining its given percentage composition.
In the exercise, we need to identify how low the molecular weight can be while keeping the sulfur percentage at 8%. This emphasizes the concept that molecular mass is ultimately influenced by the atomic masses of its constituent elements and their stoichiometry within the compound's structure.
Here’s why it matters:

• The least molecular mass ensures that the compound contains at least the minimum requirement of a specific element, based on its percentage.
• Knowing the least molecular mass can help identify unknown compounds or confirm empirical formulas.
• It acts as a check to verify if the proposed empirical formula is reasonable with the given data.

Atomic Mass

Atomic mass is a fundamental concept in chemistry that refers to the mass of an atom of a chemical element expressed in atomic mass units (amu). For calculations, it often uses the weighted average of the isotopes of an element found in nature.
In our problem, the atomic mass of sulfur is used to determine the least molecular mass of the compound. Since sulfur has an atomic mass of 32 g/mol, it contributes to calculating how it fits into the whole compound regarding its percentage presence. Using atomic masses allows chemists to compute various properties such as molecular mass and assists in stoichiometric calculations.
Remember:

• Atomic mass influences how elements combine and form compounds.
• It helps predict the behavior of a compound in reactions.
• Enables practical calculations like determining molar mass, composition analysis, and more.

Stoichiometry

Stoichiometry involves calculating and relating quantities of reactants and products in chemical reactions. It closely ties to the law of conservation of mass, whereby mass is neither created nor destroyed in a chemical reaction.
The problem uses stoichiometric principles because it involves calculations to determine the least molecular mass with the specified percentage of sulfur. It emphasizes how one can align ratios to ensure chemical equations are balanced and compounds are correctly identified.
Consider these stoichiometric connections:

• Stoichiometry allows precise measurements for chemical reactions, ensuring minimal excess and waste.
• It is essential for scaling reactions from a lab to larger production.
• Helps establish correlations between the mass of reactants and products, invaluable in research and industrial applications.