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Chapter 13: Problem 33

How many hydrogen atoms are present in \(684.6 \mathrm{g}\) of sucrose \(\left(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\right) ?\)

Short Answer

Expert verified
Answer: There are 44 hydrogen atoms present in 684.6 g of sucrose.

Step by step solution

01

Find the molecular weight of sucrose

To find the molecular weight of sucrose (C12H22O11), we calculate the sum of the atomic weights of its constituent elements, 12 Carbon atoms, 22 Hydrogen atoms, and 11 Oxygen atoms: Molecular weight of sucrose = \((12 \times 12.01) + (22 \times 1.01) + (11 \times 16.00) = 144.12 + 22.22 + 176.00 = 342.34 \mathrm{g/mol}\)
02

Calculate the number of moles of sucrose in 684.6 g

To calculate the number of moles of sucrose, we divide the given mass of sucrose (684.6 g) by its molecular weight (342.34 g/mol): Moles of sucrose = \(\frac{684.6 \mathrm{g}}{342.34 \mathrm{g/mol}} = 2.00 \mathrm{moles}\)
03

Determine the number of hydrogen atoms in one mole of sucrose

One mole of sucrose (C12H22O11) has 22 hydrogen atoms because there are 22 hydrogen atoms in the molecular formula.
04

Calculate the total number of hydrogen atoms

To find the total number of hydrogen atoms in 684.6 g of sucrose, we'll multiply the number of moles of sucrose (2 moles) by the number of hydrogen atoms in one mole of sucrose (22 hydrogen atoms). Total hydrogen atoms = \((2.00 \mathrm{moles}) \times (22 \mathrm{hydrogen\: atoms/mole}) = 44 \mathrm{hydrogen\: atoms}\) The total number of hydrogen atoms present in 684.6 g of sucrose (C12H22O11) is 44 hydrogen atoms.

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