Question

Which of the following contains the largest mass of hydrogen atoms?
A.$0.5\text{ moles }{\text{C}}_{\text{2}}{\text{H}}_{\text{2}}{\text{O}}_{\text{4}}$
B.$\text{1}\text{.1 moles }{\text{C}}_3{\text{H}}_8{\text{O}}_3$
C.$1.5\text{ moles }{\text{C}}_6{\text{H}}_8{\text{O}}_6$
D.$\text{4}\text{.0 moles }{\text{C}}_3{\text{H}}_8{\text{O}}_3$

Answer 1

Hint: A mole of a substance is the mass of a substance that contains exactly the same number of fundamental units, as in 12.0 g of C. The subscript of atom in the molecular formula indicates the number of moles of atom in one mole of formula.


Step by step answer: Calculate the mass of H atoms in$0.5\text{ moles }{\text{C}}_{\text{2}}{\text{H}}_{\text{2}}{\text{O}}_{\text{4}}$.

The molecular formula of the compound indicates that 1 mole ${\text{C}}_{\text{2}}{\text{H}}_{\text{2}}{\text{O}}_{\text{4}}$ contains 2 moles of $\text{H}$ atoms.

So, $$\text{0}\text{.5 moles }{\text{C}}_{\text{2}}{\text{H}}_{\text{2}}{\text{O}}_{\text{4}}\text{ times }{\displaystyle \frac{\text{2 mol H atom }}{1\text{ moles }{\text{C}}_{\text{2}}{\text{H}}_{\text{2}}{\text{O}}_{\text{4}}}}\text{ = 1}\text{.0 mol H atoms}$$

Now, convert these moles of $\text{H}$ atom to mass of $\text{H}$ atoms as follows:

$\text{Mass of atom = moles times atomic mass}$

The atomic mass of $\text{H}$ atom = $1.0\text{ g/mol}$

Thus,

$$\text{Mass of H atoms = 1}\text{.0 mol H atoms times 1}\text{.0 g/mol}$$

$$\text{Mass of H atoms = 1}\text{.0 g}$$

Hence, $0.5\text{ moles }{\text{C}}_{\text{2}}{\text{H}}_{\text{2}}{\text{O}}_{\text{4}}$ contain $$\text{1}\text{.0 g}$$ of $\text{H}$ atoms.

Calculate the mass of H atoms in $\text{1}\text{.1 moles }{\text{C}}_3{\text{H}}_8{\text{O}}_3$.

The molecular formula of the compound indicates that 1 mole ${\text{C}}_3{\text{H}}_8{\text{O}}_3$ contains 8 moles of $\text{H}$ atoms.

So, $$\text{1}\text{.1 moles }{\text{C}}_3{\text{H}}_8{\text{O}}_3\text{ times }{\displaystyle \frac{\text{8 mol H atom }}{1\text{ moles }{\text{C}}_3{\text{H}}_8{\text{O}}_3}}\text{ = 8}\text{.8 mol H atoms}$$

Now, convert these moles of $\text{H}$ atom to mass of $\text{H}$ atoms as follows:

$$\text{Mass of H atoms = 8}\text{.8 mol H atoms times 1}\text{.0 g/mol}$$

$$\text{Mass of H atoms = 8}\text{.8 g}$$

Hence, $\text{1}\text{.1 moles }{\text{C}}_3{\text{H}}_8{\text{O}}_3$ contain $$\text{8}\text{.8 g}$$ of $\text{H}$ atoms.

Calculate the mass of H atoms in $1.5\text{ moles }{\text{C}}_6{\text{H}}_8{\text{O}}_6$.

The molecular formula of the compound indicates that 1 mole ${\text{C}}_6{\text{H}}_8{\text{O}}_6$ contains 8 moles of $\text{H}$ atoms.

So, $$\text{1}\text{.5 moles }{\text{C}}_6{\text{H}}_8{\text{O}}_6\text{ times }{\displaystyle \frac{\text{8 mol H atom }}{1\text{ moles }{\text{C}}_3{\text{H}}_8{\text{O}}_3}}\text{ = 12 mol H atoms}$$

Now, convert these moles of $\text{H}$ atom to mass of $\text{H}$ atoms as follows:

$$\text{Mass of H atoms = 12 mol H atoms times 1}\text{.0 g/mol}$$

$$\text{Mass of H atoms = 12 g}$$

Hence, $1.5\text{ moles }{\text{C}}_6{\text{H}}_8{\text{O}}_6$ contain $$\text{12}\text{.0 g}$$ of $\text{H}$ atoms.

Calculate the mass of H atoms in $\text{4}\text{.0 moles }{\text{C}}_3{\text{H}}_8{\text{O}}_3$.

The molecular formula of the compound indicates that 1 mole ${\text{C}}_3{\text{H}}_8{\text{O}}_3$ contains 8 moles of $\text{H}$ atoms.

So, $$\text{4}\text{.0 moles }{\text{C}}_3{\text{H}}_8{\text{O}}_3\text{ times }{\displaystyle \frac{\text{8 mol H atom }}{1\text{ moles }{\text{C}}_3{\text{H}}_8{\text{O}}_3}}\text{ = 32 mol H atoms}$$

Now, convert these moles of $\text{H}$ atom to mass of $\text{H}$ atoms as follows:

$$\text{Mass of H atoms = 32 mol H atoms times 1}\text{.0 g/mol}$$

$$\text{Mass of H atoms = 32 g}$$

Hence, $\text{4}\text{.0 moles }{\text{C}}_3{\text{H}}_8{\text{O}}_3$ contain $$\text{32 g}$$ of $\text{H}$ atoms.

Now, by comparing the mass of$\text{H}$ atoms calculated for each compound we can say that $\text{4}\text{.0 moles }{\text{C}}_3{\text{H}}_8{\text{O}}_3$ contain the largest mass of hydrogen atoms.

Thus, the correct option is (D) $\text{4}\text{.0 moles }{\text{C}}_3{\text{H}}_8{\text{O}}_3$

Note: The mass of$\text{H}$ atom in compounds containing the same number of moles of H atom depends on the moles of compounds. A compound having a greater number of moles will contain a greater number of $\text{H}$ atoms and thus greater mass of H atoms.