**Mass of Carbon Atom**
In order to determine the mass of one mole of substance, we first need to establish the relative atomic mass unit based on the mass of a carbon atom. The current standard for the relative atomic mass unit is based on the carbon-12 isotope. It is defined as exactly 1/12th the mass of a carbon-12 atom. However, if we consider 1/6th instead of 1/12th, the relative atomic mass unit will change.

**Determining the Mass of One Mole**
To determine the mass of one mole of substance, we need to consider Avogadro's number, which states that one mole of any substance contains 6.022 × 10^23 particles (atoms, molecules, ions, etc.). This number is based on the carbon-12 isotope and the current definition of the relative atomic mass unit.

**Calculating the Mass of One Mole**
To calculate the mass of one mole of substance, we can use the following steps:
1. Determine the relative atomic mass unit based on 1/6th the mass of a carbon atom.
- Since the standard relative atomic mass unit is based on 1/12th the mass of a carbon-12 atom, if we consider 1/6th, the relative atomic mass unit will be 2 times larger.
- Therefore, the relative atomic mass unit will be 2 × 12 g/mol = 24 g/mol.

2. Calculate the mass of one mole of substance using the determined relative atomic mass unit.
- The mass of one mole of substance can be calculated by multiplying the relative atomic mass unit by the molar mass constant.
- The molar mass constant is defined as 1 g/mol and is equivalent to the mass of one mole of carbon-12 atoms.
- Therefore, the mass of one mole of substance will be 24 g/mol × 1 g/mol = 24 g.

**Explanation**
By considering 1/6th instead of 1/12th the mass of a carbon atom, the relative atomic mass unit will be doubled. Consequently, the mass of one mole of substance will also be doubled. This means that one mole of the substance will have a mass of 24 grams. This calculation is based on the assumption that the ratio of the masses of carbon atoms is changed from 1:12 to 1:6. However, it's important to note that the standard relative atomic mass unit is based on 1/12th the mass of a carbon-12 atom, and any deviation from this standard would lead to inconsistencies in scientific measurements and calculations.

Mass of given amount of a substance is a constant quantity that is remain unchanged.