Final answer:
To calculate the moles of K₃Fe(CN)₆ from the given number of carbon atoms, divide the total number of carbon atoms by 6 (since each molecule of K₃Fe(CN)₆ has 6 carbon atoms) and then divide by Avogadro's number. The result is 0.3 moles, which does not match any of the provided answer choices.
Step-by-step explanation:
The student has a sample of K₃Fe(CN)₆ with 1.084 x 1024 carbon atoms and they need to find out how many moles of K₃Fe(CN)₆ are in the sample. To determine the number of moles, we must use Avogadro's number, which is 6.022 x 1023 atoms/molecules per mole.
Each molecule of K₃Fe(CN)₆ contains 6 carbon atoms. To find the number of molecules of K₃Fe(CN)₆, we divide the total number of carbon atoms in the sample by 6:
1.084 x 1024 Carbon atoms / 6 Carbon atoms per molecule = 1.807 x 1023 molecules of K₃Fe(CN)₆
Next, we divide the number of molecules by Avogadro's number to find the moles of K₃Fe(CN)₆:
1.807 x 1023 molecules / 6.022 x 1023 molecules/mol = 0.3 moles of K₃Fe(CN)₆
Since the option of 0.3 moles is not provided, the student might have made an error in the number of carbon atoms, or there might be a typo in the question or the answer choices. Therefore, based on the information provided, none of the given options (a, b, c, d) are correct.