Problem: Vapour density of a metal chloride is 66. Its oxide contains 53% metal. The atomic weight of metal is?

Solution:

Step 1: Calculate the formula weight of metal chloride using its vapour density.

- The vapour density of metal chloride = 66.
- Vapour density is the ratio of the molecular weight of a gas to the weight of an equal volume of hydrogen gas under the same conditions of temperature and pressure.
- The molecular weight of hydrogen gas is 2.
- Therefore, the molecular weight of metal chloride = vapour density x 2 = 66 x 2 = 132.

Step 2: Calculate the formula weight of metal oxide.

- Metal oxide contains 53% metal.
- Therefore, the percentage of oxygen in metal oxide = 100% - 53% = 47%.
- The atomic weight of oxygen is 16.
- Therefore, the formula weight of metal oxide = (atomic weight of metal x 0.53) + (16 x 0.47).

Step 3: Equate the formula weights of metal chloride and metal oxide.

- The formula weight of metal chloride = 132 (from step 1).
- The formula weight of metal oxide = (atomic weight of metal x 0.53) + (16 x 0.47) (from step 2).
- Equating the formula weights: 132 = (atomic weight of metal x 0.53) + (16 x 0.47).
- Solving for the atomic weight of metal: atomic weight of metal = (132 - 7.52) / 0.53 = 243.77 / 0.53 = 459.54.

Answer: The atomic weight of the metal is 459.54.