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 consists of two cysteine molecules linked by a disulfide bond, and it contains two sulfur atoms. Given that the sulfur content is 26.7 percent, we can use this information to find the molecular weight of cystine.

Step-by-Step Calculation

1. Understanding the Composition

Cystine is composed of carbon (C), hydrogen (H), nitrogen (N), oxygen (O), and sulfur (S). The general formula for cystine can be represented as C₆H₁₂N₂O₄S₂. This means that in one molecule of cystine, there are:

• 6 Carbon atoms
• 12 Hydrogen atoms
• 2 Nitrogen atoms
• 4 Oxygen atoms
• 2 Sulfur atoms

2. Calculating the Molar Mass of Cystine

To find the molecular weight, we need to calculate the molar mass of each element in cystine and then sum them up:

• Carbon (C): 6 atoms × 12.01 g/mol = 72.06 g/mol
• Hydrogen (H): 12 atoms × 1.008 g/mol = 12.096 g/mol
• Nitrogen (N): 2 atoms × 14.01 g/mol = 28.02 g/mol
• Oxygen (O): 4 atoms × 16.00 g/mol = 64.00 g/mol
• Sulfur (S): 2 atoms × 32.07 g/mol = 64.14 g/mol

3. Adding It All Together

Now, we can sum these values to find the total molecular weight of cystine:

Total Molecular Weight = 72.06 + 12.096 + 28.02 + 64.00 + 64.14

Total Molecular Weight = 240.316 g/mol

4. Verifying with Sulfur Content

To ensure our calculation aligns with the given sulfur content, we can check the percentage of sulfur in cystine:

Since there are 2 sulfur atoms in cystine, the total mass of sulfur is 64.14 g/mol. The percentage of sulfur can be calculated as follows:

Sulfur Percentage = (Mass of Sulfur / Total Molecular Weight) × 100

Sulfur Percentage = (64.14 / 240.316) × 100 ≈ 26.7%

This confirms that our calculated molecular weight of cystine is accurate. Therefore, the molecular weight of cystine is approximately 240.32 g/mol.