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 for the number of moles of sodium carbonate (Na2CO3) that contain 1.773 × 10¹⁷ carbon atoms, we can break the problem into a few steps:
Step 1: Determine the number of carbon atoms in one mole of Na2CO3.
Each Na2CO3 molecule contains one carbon atom, so one mole of Na2CO3 contains 1 mole of carbon atoms.
Step 2: Use Avogadro’s number.
Avogadro’s number is 6.022 × 10²³ atoms/mole, which is the number of atoms (or molecules) in one mole of a substance.
Step 3: Set up the proportion.
We are given 1.773 × 10¹⁷ carbon atoms, and we want to find the number of moles of Na2CO3 that contain this number of carbon atoms. We can set up the following proportion:Number of moles of Na2CO3=Number of carbon atoms givenAvogadro’s number\text{Number of moles of Na2CO3} = \frac{\text{Number of carbon atoms given}}{\text{Avogadro’s number}}Number of moles of Na2CO3=Avogadro’s numberNumber of carbon atoms given
Substitute the values:Number of moles of Na2CO3=1.773×1017 atoms6.022×1023 atoms/mole\text{Number of moles of Na2CO3} = \frac{1.773 \times 10^{17} \text{ atoms}}{6.022 \times 10^{23} \text{ atoms/mole}}Number of moles of Na2CO3=6.022×1023 atoms/mole1.773×1017 atoms
Step 4: Perform the calculation.
Number of moles of Na2CO3=2.945×10−7 moles\text{Number of moles of Na2CO3} = 2.945 \times 10^{-7} \text{ moles}Number of moles of Na2CO3=2.945×10−7 moles
Conclusion:
Thus, the number of moles of sodium carbonate Na2CO3 that contain 1.773 × 10¹⁷ carbon atoms is 2.945 × 10⁻⁷ moles.
So, the correct answer is D) 2.945 × 10⁻⁷.
