Final answer:
The mass of half a mole of sucrose is 171.17 g. A quantity of 24.02 g of sucrose contains two moles of carbon atoms. If you spent a million dollars per second for 100 years, you would have left over 1 mole of dollars minus $3.1536 x 10^15.
Step-by-step explanation:
1) The molar mass of sucrose C12H22O11 is calculated by summing the atomic masses of its constituent elements: Carbon (C) has a molar mass of 12.01 g/mol, Hydrogen (H) has a molar mass of 1.01 g/mol, and Oxygen (O) has a molar mass of 16.00 g/mol. Therefore, the molar mass of sucrose is (12.01 g/mol x 12) + (1.01 g/mol x 22) + (16.00 g/mol x 11) = 342.34 g/mol. Half a mole of sucrose molecules would then be (342.34 g/mol / 2) = 171.17 g.
2) Since each sucrose molecule contains 12 carbon atoms, to find the quantity of sucrose that contains 2 moles of carbon atoms, we can calculate the molar mass of carbon (12.01 g/mol) and multiply it by the number of moles of carbon atoms (2). This gives us 12.01 g/mol x 2 mol = 24.02 g of sucrose.
3) Assuming 1 mole of dollars is equal to $6.022 x 10^23, and you spent 1 million dollars per second, we can calculate the number of seconds in 100 years: 1 year = 365 days, 1 day = 24 hours, 1 hour = 60 minutes, 1 minute = 60 seconds. Therefore, there are (100 years x 365 days/year x 24 hours/day x 60 minutes/hour x 60 seconds/minute) = 3,153,600,000 seconds in 100 years. If you spent 1 million dollars per second for that entire period, the total amount spent would be (1 million dollars/second x 3,153,600,000 seconds) = $3.1536 x 10^15. Therefore, you would have left over (1 mole of dollars - $3.1536 x 10^15).
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