A sample of glucose, \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6},\) contains \(1.250 \times 10^{21}\) carbon atoms. (a) How many atoms of hydrogen does it contain? (b) How many molecules of glucose does it contain? (c) How many moles of glucose does it contain? (d) What is the mass of this sample in grams?

Since there are 6 carbon atoms and 12 hydrogen atoms in each glucose molecule, we can find the total number of hydrogen atoms in the sample using the given number of carbon atoms. Given: \(1.250 \times 10^{21}\) carbon atoms Carbon atoms per glucose molecule: 6 Hydrogen atoms per glucose molecule: 12 Number of hydrogen atoms = (Number of carbon atoms/6) × 12 In this case, the number of hydrogen atoms: = \(\frac{(1.250 \times 10^{21})}{6} \times 12\) Now, calculate the number of hydrogen atoms: = \( 2.500 \times 10^{21}\) hydrogen atoms

To find the number of glucose molecules, we can use the given number of carbon atoms and the ratio of carbon atoms to glucose molecules. There are 6 carbon atoms in each glucose molecule, so: Number of glucose molecules = (Number of carbon atoms/6) In this case: Number of glucose molecules = \(\frac{1.250 \times 10^{21}}{6}\) Now, calculate the number of glucose molecules: = \( 2.083 \times 10^{20}\) glucose molecules

To find the number of moles of glucose in the sample, we will use Avogadro's number, which states that there are \(6.022\times 10^{23}\) particles (atoms, ions or molecules) in one mole. Number of moles of glucose = (Number of glucose molecules/Avogadro's number) = \(\frac{2.083 \times 10^{20}}{6.022 \times 10^{23}}\) Now, calculate the moles of glucose: = \( 3.459 \times 10^{-4}\) moles of glucose

To calculate the mass of the glucose sample in grams, we will use the molar mass of glucose, which can be found by adding up the molar mass of each constituent element in the glucose molecule. \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\): 12.01 g/mol (C) * 6 = 72.06 g/mol 1.01 g/mol (H) * 12 = 12.12 g/mol 16.00 g/mol (O) * 6 = 96.00 g/mol Total molar mass = 180.18 g/mol Mass of sample = (Number of moles) * (Molar mass of glucose) = \( (3.459 \times 10^{-4} \text{ moles}) \times (180.18 \text{ g/mol})\) Now, calculate the mass of the glucose sample: = \( 6.232 \times 10^{-2}\) grams The glucose sample contains: (a) \( 2.500 \times 10^{21}\) hydrogen atoms, (b) \( 2.083 \times 10^{20}\) glucose molecules, (c) \( 3.459 \times 10^{-4}\) moles of glucose, and (d) \( 6.232 \times 10^{-2}\) grams of glucose.