Question

An organic compound on analysis was found to contain \(0.032 \%\) sulphur. The molecular mass of the compound, if its molecule contains two sulphur atoms is (1) 200 (2) 2000 (3) 20,000 (4) \(2,00,000\)

Short answer

The molecular mass of the compound is 200,000 g/mol (Option 4).

Step-by-step solution

- Determine the mass percentage of sulfur

Given that the organic compound contains 0.032% sulfur, this means that in 100 grams of the compound, there are 0.032 grams of sulfur.

- Calculate mass of sulfur in one molecule

Since the molecule contains two sulfur atoms, the total mass of sulfur in one molecule is the mass of two sulfur atoms. The atomic mass of sulfur (S) is approximately 32 g/mol. Therefore, the mass of two sulfur atoms is: \[ 2 \times 32 = 64 \text{ g/mol} \]

- Relationship between mass percentage and mass in one molecule

Using the mass percentage, we know that the sulfur corresponds to 0.032% of the total molecular mass. Setting the total molecular mass to \( x \) grams, we have: \[ \frac{64}{x} \times 100 = 0.032 \]

- Solve for the molecular mass

Solving the equation from Step 3 for \( x \): \[ \frac{64}{x} \times 100 = 0.032 \] \[ \frac{64 \times 100}{0.032} = x \] \[ x = 200,000 \text{ g/mol} \]

Key concepts

Organic Compound Analysis

Organic compound analysis involves determining the composition of an organic compound. This is crucial for understanding the molecular structure and properties. One common method is to measure the amount of each element present in the compound. This can be done through techniques like combustion analysis, where the compound is burned, and the amounts of different elements are measured. In this exercise, the problem involves analyzing an organic compound to find out its sulfur content. We know that the compound contains sulfur because it was given that it has 0.032% sulfur. This percentage tells us how much sulfur is present in a given amount of the compound, such as 100 grams. Understanding these percentages helps us delve into a deeper analysis to determine the molecular mass.

Mass Percentage

Mass percentage is a method used in chemistry to describe the concentration of an element in a compound. It is calculated by comparing the mass of the element to the total mass of the compound and then multiplying by 100. In this exercise, we calculated the mass percentage of sulfur to be 0.032%.
This means in a 100 gram sample of the compound, 0.032 grams of it is sulfur.
To use this information, we expressed the mass of sulfur in terms of the total molecular mass of the compound. By setting up a proportion, we were able to solve for the total molecular mass. This step is critical because it links the given mass percentage to the actual molecular structure of the compound.

Atomic Mass of Sulfur

The atomic mass of sulfur is an essential value in many calculations. It is the average mass of sulfur atoms, taking into account the relative abundance of different isotopes in nature. For sulfur, this value is approximately 32 g/mol.
In the context of this exercise, we used it to calculate the total mass of sulfur atoms in a molecule. Since the molecule contains two sulfur atoms, the combined mass is \( 2 \times 32 = 64 \) grams.
This mass was then related to the molecular mass of the whole compound. The key was to use the mass percentage we found earlier, to set up an equation and solve for the total molecular mass. Knowing atomic masses like that of sulfur enables such calculations, making it a vital concept in chemistry.