100g of a diatomic molecule, Z2, reacts with water to form 74 .0 g of ZOH and 51.4 g of ZH. Calculate the relative atomic mass and hence the identity of Z.

To solve this problem, we need to use the law of conservation of mass which states that matter cannot be created or destroyed.

Step 1: Calculate the mass of Z in Z2 The mass of Z2 is 100g. Since it's a diatomic molecule, it means it's made up of two atoms of Z. Therefore, the mass of Z in Z2 is 100g/2 = 50g.

Step 2: Calculate the mass of Z in ZOH and ZH The mass of Z in ZOH is 74.0g - mass of O - mass of H. The atomic masses of O and H are approximately 16g and 1g respectively. Therefore, the mass of Z in ZOH is 74.0g - 16g - 1g = 57g. The mass of Z in ZH is 51.4g - mass of H = 51.4g - 1g = 50.4g.

Step 3: Calculate the average mass of Z The average mass of Z is (mass of Z in Z2 + mass of Z in ZOH + mass of Z in ZH) / 3 = (50g + 57g + 50.4g) / 3 = 52.47g.

Step 4: Identify Z The relative atomic mass of Z is approximately 52.47, which is close to the atomic mass of chromium (Cr), 52. Therefore, Z is chromium (Cr).