Question

1. sample a: 1 mole of carbon dioxide (co₂) molecules sample b: 1 mole of carbon atoms sample c: 1 mole of glucose (c₆h₁₂o₆) molecules which of the following statements is true about samples a, b, and c? all the samples are the same mass all the samples have the same volume all the samples contain the same number of carbon atoms. all the samples contain 6.02×10²³ particles

Explanation:

Step1: Recall Avogadro's number

Avogadro's number \(N_A = 6.02\times 10^{23}\) particles per mole.

Step2: Analyze each sample

• Sample A: 1 mole of \(CO_2\) molecules. By Avogadro's number, it has \(6.02\times 10^{23}\) \(CO_2\) molecules.
• Sample B: 1 mole of carbon atoms. By Avogadro's number, it has \(6.02\times 10^{23}\) carbon atoms.
• Sample C: 1 mole of \(C_6H_{12}O_6\) molecules. By Avogadro's number, it has \(6.02\times 10^{23}\) \(C_6H_{12}O_6\) molecules.

Step3: Analyze mass

• Molar mass of \(CO_2\): \(M_{CO_2}=44\space g/mol\) ( \(M = 12+2\times16\) ).
• Molar mass of \(C\): \(M_{C}=12\space g/mol\).
• Molar mass of \(C_6H_{12}O_6\): \(M_{C_6H_{12}O_6}=180\space g/mol\) ( \(M=6\times12 + 12\times1+6\times16\) ). So, masses are different.

Step4: Analyze volume (for gases at same \(T\) and \(P\), \(V = nRT/P\), but \(C\) is solid, \(C_6H_{12}O_6\) is solid or in solution)

• \(CO_2\) is a gas (at standard conditions), \(C\) is solid, \(C_6H_{12}O_6\) is solid (or in solution). Volumes are different.

Step5: Analyze number of carbon atoms

• Sample A: 1 mole \(CO_2\) has 1 mole \(C\) atoms (\(6.02\times 10^{23}\) \(C\) atoms).
• Sample B: 1 mole \(C\) atoms (\(6.02\times 10^{23}\) \(C\) atoms).
• Sample C: 1 mole \(C_6H_{12}O_6\) has 6 moles \(C\) atoms (\(6\times6.02\times 10^{23}\) \(C\) atoms). So, number of \(C\) atoms are different.

Answer:

All the samples contain \(6.02\times 10^{23}\) particles.