Question

A membrane consists of 50% protein and 50% phosphoglycerides by weight. The average molecular weights of the lipids and proteins are 800 Da and 50 kDa respectively. The molar ratio of lipid to protein in this membrane is:

• A. 62.50
• B. 6.25
• C. 0.625
• D. 0.0625

Hint:

Even if a membrane is 50-50 by weight, the number of lipid molecules is much higher because they are much smaller than proteins.
Always convert kiloDaltons (kDa) to Daltons (Da) by multiplying by 1000 before starting calculations!

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
The question asks for the molar ratio of lipids to proteins in a biological membrane, given their weight percentages and their respective average molecular weights.
Key Formula or Approach:
1. Assume a total mass of the membrane (e.g., 100 grams).
2. Calculate the number of moles for each component using the formula:
\[ \text{Number of moles (n)} = \frac{\text{Mass (m)}}{\text{Molecular Weight (MW)}} \]
3. Find the ratio of the moles of lipid to the moles of protein.

Step 2: Detailed Explanation:

• Given Data:
- Protein content = 50% by weight.
- Lipid (phosphoglyceride) content = 50% by weight.
- Average MW of Protein = 50 kDa = $50,000$ Da (g/mol).
- Average MW of Lipid = 800 Da (g/mol).

• Assuming a 100g sample:
- Mass of protein ($m_p$) = 50 g.
- Mass of lipid ($m_l$) = 50 g.

• Calculating Moles:
- Moles of protein ($n_p$) = $\frac{50}{50,000} = 0.001$ moles.
- Moles of lipid ($n_l$) = $\frac{50}{800} = 0.0625$ moles.

• Calculating Molar Ratio:
- Molar ratio (Lipid : Protein) = $\frac{n_l}{n_p}$
- Ratio = $\frac{0.0625}{0.001} = 62.5$.

Step 3: Final Answer:
The molar ratio of lipid to protein in the membrane is 62.50, meaning there are 62.5 lipid molecules for every 1 protein molecule.