Final answer:
To find the molecular weight of substance X, we use the concept of isotonic solutions, where a 10% urea solution is isotonic with a 20% solution of substance X. The calculation involves setting up a proportion based on the mass percent and known molecular weight of urea (60 g/mol), resulting in a molecular weight of 120 g/mol for substance X.
Step-by-step explanation:
To calculate the molecular weight of substance X, we must use the concept of osmotic pressure, considering a 10% solution of urea is isotonic with a 20% solution of substance X. Isotonic solutions have the same osmotic pressure, which implies that they have the same number of particles, or moles, in a given volume of solution.
The molecular weight (MW) of urea is approximately 60 g/mol, so a 10% solution means 10 grams of urea per 100 mL of solution, or 0.1 grams per mL.
Since the solutions are isotonic, we can set up a proportion based on the ratio of mass percent to molecular weight to find the molecular weight of X:
- (Mass percent of urea / MW of urea) = (Mass percent of X / MW of X)
- (10% / 60 g/mol) = (20% / MW of X)
- (0.10 / 60) = (0.20 / MW of X)
- MW of X = (0.20 * 60) / 0.10
- MW of X = 120 g/mol
Therefore, the molecular weight of substance X is 120 g/mol.