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Five calcite, CaCO₃ (MM 100.085 g/mol), samples of equal mass have a total mass of 10.1±0.1 g. What is the average mass and absolute uncertainty of calcium in each sample? Assume that the relative uncertainties in atomic mass are small compared to the uncertainty of the total mass.

User Literal
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Final answer:

The average mass and absolute uncertainty of calcium in each calcite sample are calculated by determining the fraction of calcium in CaCO3 and applying it to the total mass and its uncertainty respectively.

Step-by-step explanation:

To calculate the average mass and absolute uncertainty of calcium in each calcite (CaCO3) sample, we first determine the average mass of each of the five samples by dividing the total mass by the number of samples:

Average mass of each sample = Total mass of samples / Number of samples

Average mass of each sample = 10.1 g / 5 = 2.02 g

Then we calculate the fraction of calcium in calcium carbonate. From the molar mass of CaCO3 (100.085 g/mol) and calcium (Ca, approximately 40.078 g/mol), the fraction can be determined. The molar mass of Ca divided by the molar mass of CaCO3 gives us:

Fraction of Ca in CaCO3 = Molar mass of Ca / Molar mass of CaCO3

Fraction of Ca in CaCO3 = 40.078 g/mol / 100.085 g/mol

We can now find the mass of calcium in one sample of CaCO3 by multiplying the fraction by the average mass of a sample:

Mass of Ca in one sample = Fraction of Ca in CaCO3 × Average mass of each sample

The absolute uncertainty in the mass of calcium for each sample is the original absolute uncertainty (0.1 g) divided by the number of samples, which is in turn multiplied by the fraction of calcium in CaCO3.

Absolute uncertainty of Ca in one sample = (Absolute uncertainty of total / Number of samples) × Fraction of Ca in CaCO3

Note: The assumption made here is that the relative uncertainties in atomic mass are small and can be ignored, focusing solely on the uncertainty of the total mass provided.

User Ilya Kushlianski
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