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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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Most popular questions from this chapter

At \(0.0^{\circ} \mathrm{C}\) and \(1.00 \mathrm{atm}, 1.00 \mathrm{mol}\) of a gas occupies a volume of \(0.0224 \mathrm{m}^{3} .\) (a) What is the number density? (b) Estimate the average distance between the molecules. (c) If the gas is nitrogen \(\left(\mathrm{N}_{2}\right),\) the principal component of air, what is the total mass and mass density?

A bubble rises from the bottom of a lake of depth \(80.0 \mathrm{m},\) where the temperature is \(4^{\circ} \mathrm{C} .\) The water temperature at the surface is \(18^{\circ} \mathrm{C} .\) If the bubble's initial diameter is \(1.00 \mathrm{mm},\) what is its diameter when it reaches the surface? (Ignore the surface tension of water. Assume the bubble warms as it rises to the same temperature as the water and retains a spherical shape. Assume \(\left.P_{\mathrm{atm}}=1.0 \mathrm{atm} .\right)\)

The mass density of diamond (a crystalline form of carbon) is \(3500 \mathrm{kg} / \mathrm{m}^{3} .\) How many carbon atoms per \(\mathrm{cm}^{3}\) are there?
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