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

To determine the molecular weight of cystine based on its sulfur content, we can use the information provided about the percentage of sulfur and the fact that cystine contains two sulfur atoms. Let's break this down step by step.

Understanding the Composition of Cystine

Cystine is a naturally occurring amino acid that is formed when two cysteine molecules bond together through a disulfide bond. The molecular formula for cystine is C₆H₁₂N₂O₄S₂, indicating that it contains carbon, hydrogen, nitrogen, oxygen, and sulfur. The key point here is that cystine has two sulfur atoms, which contribute to its overall molecular weight.

Calculating the Molecular Weight

We know that the sulfur content in cystine is 26.7 percent. This means that if we consider 100 grams of cystine, 26.7 grams of that would be sulfur. Since cystine contains two sulfur atoms, we can calculate the molecular weight as follows:

• The atomic weight of sulfur (S) is approximately 32.07 g/mol.
• Since there are two sulfur atoms in cystine, the total weight contributed by sulfur is: 2 × 32.07 g/mol = 64.14 g/mol.

Now, if 26.7 grams of sulfur corresponds to 100 grams of cystine, we can set up a proportion to find the total molecular weight of cystine:

• Let M be the molecular weight of cystine.
• Using the proportion: 64.14 g (sulfur) / M (molecular weight of cystine) = 26.7 g (sulfur) / 100 g (cystine).

Solving for M

Cross-multiplying gives us:

• 64.14 g × 100 g = 26.7 g × M
• 6414 = 26.7M
• M = 6414 / 26.7
• M ≈ 240.45 g/mol

Final Thoughts

Therefore, the approximate molecular weight of cystine is around 240.45 g/mol. This calculation not only highlights the significance of sulfur in cystine but also demonstrates how to use percentage composition to derive molecular weights. Understanding these relationships is crucial in biochemistry, especially when studying amino acids and proteins.

To determine the molecular weight of cystine based on its sulfur content, we can use the information provided about the percentage of sulfur and the number of sulfur atoms in the molecule. Let's break this down step by step.

Understanding Cystine's Composition

Cystine is an amino acid that is formed by the oxidation of two cysteine molecules, and it contains two sulfur atoms in its structure. The sulfur content is given as 26.7 percent. This means that in a sample of cystine, 26.7% of its mass is due to sulfur.

Setting Up the Calculation

To find the molecular weight, we can set up a simple equation. Let's denote the molecular weight of cystine as \( M \). Since sulfur makes up 26.7% of cystine, we can express this mathematically:

• Mass of sulfur in cystine = 0.267 * M

Since there are two sulfur atoms in cystine, we can also express the mass of sulfur in terms of the atomic weight of sulfur. The atomic weight of sulfur (S) is approximately 32 grams per mole. Therefore, the total mass of sulfur in cystine can also be expressed as:

• Mass of sulfur = 2 * 32 g/mol = 64 g/mol

Creating the Equation

Now we can set these two expressions for the mass of sulfur equal to each other:

• 0.267 * M = 64

Solving for Molecular Weight

To find \( M \), we can rearrange the equation:

• M = 64 / 0.267

Now, performing the division:

• M ≈ 239.3 g/mol

Final Thoughts

Thus, the approximate molecular weight of cystine is around 239.3 grams per mole. This calculation illustrates how we can use the percentage composition of an element in a compound to derive its molecular weight, which is a fundamental concept in chemistry.