How many moles of sodium carbonate Na2CO3 contain 1.773 * 10^17 carbon atoms? A) 8.836 * 10^-7 B) 5.590 * 10^-7 C) 1.473 * 10^-7 D) 2.945 * 10^-7
The Correct Answer and Explanation is:
To solve this, we can use the concept of Avogadro’s number and stoichiometry. Here’s the step-by-step solution:
- Determine the relationship between carbon atoms and moles of sodium carbonate: Sodium carbonate (Na₂CO₃) contains 1 carbon atom per formula unit. Therefore, the number of moles of sodium carbonate will be directly related to the number of moles of carbon atoms present.
- Convert carbon atoms to moles of carbon: Avogadro’s number (6.022 × 10²³ atoms/mol) tells us how many atoms there are in one mole of a substance. To find the number of moles of carbon atoms, use the following relation: Moles of carbon=Number of carbon atomsAvogadro’s number=1.773×10176.022×1023\text{Moles of carbon} = \frac{\text{Number of carbon atoms}}{\text{Avogadro’s number}} = \frac{1.773 \times 10^{17}}{6.022 \times 10^{23}} Moles of carbon=Avogadro’s numberNumber of carbon atoms=6.022×10231.773×1017 Let’s perform this calculation: Moles of carbon=1.773×10176.022×1023=2.945×10−7 moles of carbon\text{Moles of carbon} = \frac{1.773 \times 10^{17}}{6.022 \times 10^{23}} = 2.945 \times 10^{-7} \text{ moles of carbon}Moles of carbon=6.022×10231.773×1017=2.945×10−7 moles of carbon
- Calculate the moles of sodium carbonate: Since each Na₂CO₃ unit contains 1 carbon atom, the number of moles of sodium carbonate is the same as the number of moles of carbon. Therefore: Moles of sodium carbonate=2.945×10−7 moles\text{Moles of sodium carbonate} = 2.945 \times 10^{-7} \text{ moles}Moles of sodium carbonate=2.945×10−7 moles
Thus, the correct answer is D) 2.945 × 10⁻⁷.
Explanation:
- The key concept here is the 1:1 ratio of carbon atoms to sodium carbonate formula units in Na₂CO₃. This makes the calculation straightforward: the number of moles of carbon atoms directly translates to the number of moles of sodium carbonate.
- Using Avogadro’s number allows us to relate the count of individual atoms to macroscopic quantities (moles).
