The sulphur content of cystine is 26.7 percent. given that cystine contains two sulphur atoms, what is the molecular weight of cystine?

To determine the molecular weight of cystine based on its sulfur content, we can follow a systematic approach. Cystine is an amino acid that contains two sulfur atoms in its structure, and knowing the percentage of sulfur helps us calculate its molecular weight. Let's break this down step by step.

Understanding the Composition of Cystine

Cystine is formed by the oxidation of two cysteine molecules, and its chemical formula is C₆H₁₂N₂O₄S₂. This indicates that cystine consists of carbon, hydrogen, nitrogen, oxygen, and sulfur. The key here is to focus on the sulfur content, which is given as 26.7 percent.

Calculating the Molecular Weight

To find the molecular weight of cystine, we can use the percentage of sulfur to set up an equation. The molecular weight of sulfur (S) is approximately 32.07 g/mol. Since cystine contains two sulfur atoms, the total contribution of sulfur to the molecular weight is:

• Weight of sulfur in cystine = 2 × 32.07 g/mol = 64.14 g/mol

Now, if sulfur constitutes 26.7% of the total molecular weight (let's denote the molecular weight of cystine as M), we can express this relationship mathematically:

• 0.267 × M = 64.14 g/mol

Solving for M

To find M, we can rearrange the equation:

• M = 64.14 g/mol / 0.267

Now, performing the calculation:

• M ≈ 240.5 g/mol

Final Thoughts

Thus, the molecular weight of cystine is approximately 240.5 g/mol. This calculation illustrates how we can use the percentage composition of an element within a compound to derive its overall molecular weight. Understanding these relationships is crucial in fields like biochemistry and molecular biology, where precise measurements of molecular weights are essential for various applications.