Suppose the atomic mass unit had been defined as 1/10 th of the average mass of an atom of phosphorus. What would the atomic mass of Carbon be on this scale. What would Avogadro's number be?
It is now 1/12 of atom C12 = 1/12 x 12 = 1.0 and 1.0/6.02E23 = 1.66E-24 grams for 1 amu.
If 1/10 P31 then 1/10 x 31 = 31/10 and
31/10 x 1/6.02E23 = 5.15E-24 g = 1 amu.
Check my thinking.
To answer this question, we need to know the atomic mass of phosphorus and the atomic mass of carbon on the hypothetical scale where the atomic mass unit (amu) is defined as 1/10th of the average mass of an atom of phosphorus.
Let's assume the atomic mass of phosphorus on this scale is X amu.
Since the atomic mass unit is defined as 1/10th of the average mass of an atom of phosphorus, we can say that 1 amu is equal to 1/10th of X amu.
Therefore, 1 amu = (1/10)X amu.
Now, to find the atomic mass of carbon on this scale, we need to consider the mass ratio between carbon and phosphorus.
The atomic mass of carbon relative to phosphorus is approximately 12:31. This means that the mass of a carbon atom is roughly 12/31 times the mass of a phosphorus atom.
So, the atomic mass of carbon on this scale would be:
Mass of carbon = (12/31) * X amu.
To determine Avogadro's number on this hypothetical scale, we need to consider the relationship between the mass of one mole of a substance and Avogadro's number.
Avogadro's number, denoted as N, is defined as the number of entities (atoms, molecules, or ions) in one mole of a substance.
On the conventional scale, the atomic mass unit is defined as 1/12th of the mass of a carbon-12 atom. Therefore, one mole of carbon-12 atoms has a mass of exactly 12 grams, and there are Avogadro's number of atoms in 12 grams.
On the hypothetical scale, the atomic mass unit is defined as 1/10th of X amu (the mass of a phosphorus atom). Therefore, one mole of phosphorus atoms would have a mass of 10X grams, and there would be N (the hypothetical Avogadro's number) atoms in 10X grams.
From the above, we can set up the following ratio:
N/N₀ = mass₁/mass₀
Here, N₀ represents the conventional Avogadro's number and mass₀ represents the conventional molar mass. N represents the hypothetical Avogadro's number and mass₁ represents the hypothetical molar mass.
Plugging in the known values, we have:
N/N₀ = (10X grams)/(12 grams)
Simplifying:
N/N₀ = 10X/12
Therefore, Avogadro's number on this hypothetical scale would be:
N = N₀ * (10X/12)
Please note that these values are hypothetical and have been assumed for the purpose of this explanation. The actual values are based on the current definitions and measurements of atomic masses and Avogadro's number.