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Chapter 3: Problem 30

(a) What is the mass, in grams, of a mole of \({ }^{12} \mathrm{C}\) ? (b) How many carbon atoms are present in a mole of \({ }^{12} \mathrm{C}\) ?

Short Answer

Expert verified
a) The mass of one mole of \({ }^{12} \mathrm{C}\) in grams is 12 grams. b) There are approximately \(6.022 \times 10^{23}\) carbon atoms present in one mole of \({ }^{12} \mathrm{C}\).

Step by step solution

01

Find the atomic mass of \({ }^{12} \mathrm{C}\)

The given carbon isotope is \({ }^{12} \mathrm{C}\) which means its atomic mass (Carbon-12) is approximately 12 atomic mass units (amu).
02

Convert the atomic mass to grams

To find the mass in grams of one mole of \({ }^{12} \mathrm{C}\), we will first need to convert the atomic mass from amu to grams. The conversion factor is 1 mole of a substance = the substance's Atomic Mass in grams. In this case, 1 mole of \({ }^{12} \mathrm{C}\) = 12 grams.
03

Determine the mass of one mole of \({ }^{12} \mathrm{C}\) in grams#a)

From our calculation in Step 2, we know that 1 mole of \({ }^{12} \mathrm{C}\) = 12 grams. So, the mass of one mole of \({ }^{12} \mathrm{C}\) in grams is 12 grams.
04

Find Avogadro's number

Avogadro's number represents the number of atoms in one mole of a substance. It is equal to approximately \(6.022 \times 10^{23}\) atoms/mol.
05

Calculate the number of carbon atoms in one mole of \({ }^{12} \mathrm{C}\)

By using Avogadro's number, we can calculate the number of carbon atoms in one mole of \({ }^{12} \mathrm{C}\). Number of carbon atoms = (1 mole of \({ }^{12} \mathrm{C}\)) \(\times\) (\(6.022 \times 10^{23}\) atoms/mol) b) Therefore, there are approximately \(6.022 \times 10^{23}\) carbon atoms present in one mole of \({ }^{12} \mathrm{C}\).

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