Given that the molar mass of CO_2 is 44 g/mol, how many moles of CO_2 are present in 27 billion tons (2.7 × 10^{10} tons)? (1 ton = 1 × 10^6 g)

• A. 6.1 × 10^{14} moles
• B. 2.7 × 10^{10} moles
• C. 4.5 × 10^{15} moles
• D. 1.2 × 10^{12} moles

Answer: (A)

Verified step by step guidance

1. Convert the mass of CO_2 from tons to grams using the conversion factor: 1 ton = 1 \times 10^{6} g. Multiply the given mass in tons by this factor to get the mass in grams. Mathematically, this is: \(\text{mass in grams} = 2.7 \times 10^{10} \text{ tons} \times 1 \times 10^{6} \frac{\text{g}}{\text{ton}}\).
2. Recall the formula to calculate moles from mass and molar mass: \(\text{moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}}\).
3. Use the given molar mass of CO_2, which is 44 g/mol, and divide the mass in grams (from step 1) by this molar mass to find the number of moles: \(\text{moles of CO}_2 = \frac{\text{mass in grams}}{44}\).
4. Perform the division carefully, keeping track of the powers of ten to maintain scientific notation accuracy.
5. Express the final answer in scientific notation to match the format of the provided options.