Consider a sample of 10.0 g of the gaseous hydrocarbon C2H6 to answer the following question: How many carbon atoms are present in a 10.0 g sample? (The question is asking for the number of carbons in the sample, not the molecule).
When answering the question, include the following:
- State how to find the number of atoms for carbon in a 10.0 g sample.
- State how you know if you need to multiply or divide by Avogadro’s number.
- Give the correct number of significant figures and explain why the answer has that many significant figures.
- Give the numerical answer.
Do I multiply 10 as if I were figuring out the problem just being C2H6?
find moles ... 10.0 g / molar mass
there are two C atoms per molecule
... two moles of C for each mole of C2H6
moles of C = 2 * (moles of C2H6)
C atoms = (moles C) * (Avogadro's number)
To find the number of carbon atoms in a 10.0 g sample of C2H6, you can use the concept of moles and Avogadro's number.
1. Start by determining the molar mass of C2H6 (ethane).
The molecular formula of C2H6 shows that it contains 2 carbon atoms, so we need to calculate the molar mass of carbon and multiply it by 2. Looking up the atomic mass of carbon on the periodic table, we find that it is approximately 12.01 g/mol. Therefore, the molar mass of carbon in C2H6 is 2 * 12.01 g/mol = 24.02 g/mol.
2. Determine the number of moles of C2H6 in the given 10.0 g sample.
To do this, divide the given mass of the sample by the molar mass of C2H6.
Number of moles of C2H6 = 10.0 g / 24.02 g/mol = 0.416 moles.
3. Multiply the number of moles of C2H6 by the number of carbon atoms in one mole of C2H6.
Since C2H6 has 2 carbon atoms in one mole, multiply the number of moles by 2 to find the number of carbon atoms.
Number of carbon atoms = 0.416 moles * 2 = 0.832 moles.
4. Determine whether to multiply or divide by Avogadro's number.
To convert from moles to individual particles (atoms), you need to multiply the number of moles by Avogadro's number (6.022 x 10^23 atoms/mol). In this case, C2H6 is a sample of molecules, not individual atoms, so we need to multiply the number of moles by Avogadro's number.
Number of carbon atoms = 0.832 moles * (6.022 x 10^23 atoms/mol) = 5.01 x 10^23 atoms.
5. Determine the correct number of significant figures.
The numerical answer, 5.01 x 10^23 atoms, should have three significant figures since the original mass of the sample, 10.0 g, has three significant figures.
Therefore, the answer to the question "How many carbon atoms are present in a 10.0 g sample?" is 5.01 x 10^23 carbon atoms.