Final answer:
In 15.0 kmol of xylene (C6H6), there are approximately 0.6249 kg of xylene, 9.033 × 10^24 mol of xylene, 6803.886 lb-mole of xylene, 7.2264 × 10^25 mol of carbon (g-atom), 9.033 × 10^25 mol of hydrogen, 8.677 × 10^26 g of carbon, 9.099 × 10^26 g of hydrogen, and 5.442 × 10^48 molecules of C6H6.
Step-by-step explanation:
To determine the quantities of each component in 15.0 kmol of xylene, we need to consider the chemical formula of xylene, which is C8H10.
- a) To find the mass of xylene in kg, we can use the molar mass of xylene: (8 mol C6H6)(78.1139 g/mol) = 624.9112 g C6H6. Converting grams to kg, we have 624.9112 g ÷ 1000 = 0.6249 kg C6H6.
- b) To determine the number of moles of xylene, we can use the formula: n = N × Avogadro's number, where N is the number of kmol and Avogadro's number is 6.022 × 10^23 mol^-1. Thus, (15.0 kmol)(6.022 × 10^23 mol^-1) = 9.033 × 10^24 mol C6H6.
- c) To convert kmol to lb-mole, we can use the conversion factor 1 lb-mole = 453.5924 mol. Therefore, (15.0 kmol)(453.5924 mol/lb-mole) = 6803.886 mol C6H6.
- d) The number of moles of g-atom C is equal to the number of moles of xylene multiplied by the number of atoms of C in xylene's molecular formula: (9.033 × 10^24 mol)(8) = 7.2264 × 10^25 mol.
- e) In the same way as part d, we can calculate the number of moles of H in xylene: (9.033 × 10^24 mol)(10) = 9.033 × 10^25 mol.
- f) To find the mass of carbon, we can use the molar mass of carbon and the number of moles of C in xylene: (7.2264 × 10^25 mol)(12.0107 g/mol) = 8.677 × 10^26 g C.
- g) Similar to part f, we can determine the mass of hydrogen: (9.033 × 10^25 mol)(1.00784 g/mol) = 9.099 × 10^26 g H.
- h) To find the number of C6H6 molecules, we can use Avogadro's number and the number of moles of xylene: (9.033 × 10^24 mol)(6.022 × 10^23 molecules/mol) = 5.442 × 10^48 molecules of C6H6.