Question

Convert the following to moles. (a) \(4.00 \times 10^{3} \mathrm{~g}\) of hydrazine, a rocket propellant (b) \(12.5 \mathrm{~g}\) of tin(II) fluoride, the active ingredient in fluoride toothpaste (c) \(13 \mathrm{~g}\) of caffeine, \(\mathrm{C}_{4} \mathrm{H}_{5} \mathrm{~N}_{2} \mathrm{O}\)

Short answer

Question: Convert the given mass of each substance to moles: (a) 4.00 × 10³g of hydrazine (N₂H₄) (b) 12.5g of tin(II) fluoride (SnF₂) (c) 13g of caffeine (C₄H₅N₂O) Answer: (a) 124.8 moles of hydrazine (N₂H₄) (b) 0.0797 moles of tin(II) fluoride (SnF₂) (c) 0.158 moles of caffeine (C₄H₅N₂O)

Step-by-step solution

Find the molar mass of hydrazine (N\(_2\)H\(_4\))

To find the molar mass of hydrazine, add the molar masses of the elements within the compound: In hydrazine, there are 2 nitrogen atoms (each with a molar mass of 14.01 g/mol) and 4 hydrogen atoms (each with a molar mass of 1.008 g/mol). So, the molar mass of hydrazine (N\(_2\)H\(_4\)) is (2 × 14.01) + (4 × 1.008) = 32.048 g/mol.

Convert the mass of hydrazine to moles

Using the formula we discussed in the analysis, we obtain: moles of hydrazine = \(\frac{4.00 \times 10^{3} \mathrm{~g}}{32.048 \mathrm{~g/mol}} = 124.8 \,\text{moles of }N_{2}H_{4}\).

Find the molar mass of tin(II) fluoride (SnF\(_2\))

Tin(II) fluoride has 1 tin atom (molar mass 118.71 g/mol) and 2 fluorine atoms (molar mass 19.00 g/mol). The total molar mass is: (1 × 118.71) + (2 × 19.00) = 156.71 g/mol.

Convert the mass of tin(II) fluoride to moles

Using the formula, we calculate: moles of tin(II) fluoride = \(\frac{12.5\mathrm{~g}}{156.71\mathrm{~g/mol}} = 0.0797 \,\text{moles of } SnF_{2}\).

Find the molar mass of caffeine (C\(_4\)H\(_5\)N\(_2\)O)

The molar mass of caffeine can be found by adding up the molar masses of the elements within the compound: 4 carbon atoms (molar mass 12.01 g/mol), 5 hydrogen atoms (molar mass 1.008 g/mol), 2 nitrogen atoms (molar mass 14.01 g/mol), and 1 oxygen atom (molar mass 16.00 g/mol). The molar mass of caffeine (C\(_4\)H\(_5\)N\(_2\)O) is (4 × 12.01) + (5 × 1.008) + (2 × 14.01) + (1 × 16.00) = 82.09 g/mol.

Convert the mass of caffeine to moles

Applying the formula again, we obtain: moles of caffeine = \(\frac{13\mathrm{~g}}{82.09\mathrm{~g/mol}} = 0.158 \,\text{moles of } C_{4}H_{5}N_{2}O\). To summarize, the conversion of mass to moles for each substance is as follows: (a) 124.8 moles of hydrazine (N\(_2\)H\(_4\)) (b) 0.0797 moles of tin(II) fluoride (SnF\(_2\)) (c) 0.158 moles of caffeine (C\(_4\)H\(_5\)N\(_2\)O)