Questions: Cinnamaldehyde (C9H8O) gives cinnamon its characteristic flavor and is an important component in the popular "pumpkin spice" drinks and desserts. Calculate the number of molecules in a 0.826 g sample of pure cinnamaldehyde. - Report your answer to 2 decimal places. - Report your answer in scientific notation. - The left box corresponds to the decimal part of the number. (Example: type 5.6 for the answer 5.6 × 10^3 ) - The right box corresponds to the exponent. (Example: type 3 for the answer 5.6 × 10^3 ) type your answer. × 10 type your answermolecules of C9H8O

Solution Steps

The molecular formula for cinnamaldehyde is \(\mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}\). To find the molar mass, we sum the atomic masses of all the atoms in the formula:

• Carbon (C): \(9 \times 12.01 \, \text{g/mol} = 108.09 \, \text{g/mol}\)
• Hydrogen (H): \(8 \times 1.008 \, \text{g/mol} = 8.064 \, \text{g/mol}\)
• Oxygen (O): \(1 \times 16.00 \, \text{g/mol} = 16.00 \, \text{g/mol}\)

Adding these together gives the molar mass of cinnamaldehyde: \[ 108.09 + 8.064 + 16.00 = 132.154 \, \text{g/mol} \]

Using the mass of the sample and the molar mass, we calculate the number of moles of cinnamaldehyde in the sample: \[ \text{moles} = \frac{\text{mass}}{\text{molar mass}} = \frac{0.826 \, \text{g}}{132.154 \, \text{g/mol}} = 0.006252 \, \text{mol} \]

To find the number of molecules, we use Avogadro's number, \(6.022 \times 10^{23} \, \text{molecules/mol}\): \[ \text{molecules} = 0.006252 \, \text{mol} \times 6.022 \times 10^{23} \, \text{molecules/mol} = 3.764 \times 10^{21} \, \text{molecules} \]

Final Answer