Five mineral samples of equal mass of calcite, CaCO3 (MM 100.085) , had a total mass of 12.4 ± 0.1 g. What is the average mass of calcium in each sample?

(Assume that the relative uncertainties in atomic mass are small compared the uncertainty of the total mass.)
(Input the answer in terms of absolute uncertainty.)

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To find the average mass of calcium in each sample, we first need to determine the mass of calcium in all the samples combined, and then divide it by the number of samples.

Given:
- Total mass of the five mineral samples = 12.4 ± 0.1 g
- Molecular mass of calcite (CaCO3) = 100.085 g/mol
- We need to find the average mass of calcium in each sample

First, let's calculate the molar mass of calcium (Ca) by subtracting the molar mass of CO3 (carbonate ion) from the molar mass of calcite:

Molar mass of Ca = Molar mass of CaCO3 - Molar mass of CO3
= 100.085 g/mol - (12.01 g/mol + 3 * 16.00 g/mol) (Since CO3 has one carbon atom and three oxygen atoms)
= 40.08 g/mol

Next, let's calculate the total moles of calcium in the five samples:

Total moles of Ca = (Total mass of samples) / (Molar mass of Ca)
= (12.4 g ± 0.1 g) / (40.08 g/mol) (Using the given total mass and calcium's molar mass)

Now, to find the average mass of calcium in each sample, we need to divide the total mass of calcium by the number of samples. Since we have five samples, the average mass of calcium in each sample is:

Average mass of Ca in each sample = (Total mass of Ca) / (Number of samples)
= (Total moles of Ca) * (Molar mass of Ca) / (Number of samples)
= (12.4 g ± 0.1 g) / (40.08 g/mol) * 40.08 g/mol / 5

Simplifying the equation:
Average mass of Ca in each sample = 12.4 g ± 0.1 g / 5

Therefore, the average mass of calcium in each sample is 2.48 g ± 0.02 g.