The mass of 6 million molecules of a diatomic gas is 5.1  × 10-19 kg. What is the atomic mass of the element in this gas?

Sure, here are the steps to solve this problem:

1. First, we need to understand that a diatomic gas means it's composed of molecules that contain two atoms each. So, 6 million molecules of a diatomic gas would contain 12 million atoms.

2. Next, we need to convert the mass of the 6 million molecules from kilograms to atomic mass units (amu), because atomic masses are usually expressed in amu. 1 amu is approximately equal to 1.66 × 10^-27 kg. So, we divide the given mass by the conversion factor to get the total mass in amu.

   5.1 × 10^-19 kg / 1.66 × 10^-27 kg/amu = approximately 307228915662650.6 amu

3. Now, we divide this total mass by the total number of atoms to find the atomic mass of one atom.

   307228915662650.6 amu / 12 million atoms = approximately 25.6 amu

So, the atomic mass of the element in this gas is approximately 25.6 amu.