Naphthalene, C10H8, an ingredient in mothballs, has a molar mass of 128.18 g/mol. How many molecules of naphthalene are in a mothball that has 6.000 g of naphthalene?
The Correct Answer and Explanation is:1
To find the number of molecules of naphthalene in a mothball, we can use the following steps:
Step 1: Calculate the number of moles of naphthalene
We are given the mass of naphthalene as 6.000 g and its molar mass as 128.18 g/mol. To calculate the number of moles of naphthalene, we use the formula:moles of naphthalene=mass of naphthalenemolar mass of naphthalene\text{moles of naphthalene} = \frac{\text{mass of naphthalene}}{\text{molar mass of naphthalene}}moles of naphthalene=molar mass of naphthalenemass of naphthalene
Substituting the given values:moles of naphthalene=6.000 g128.18 g/mol=0.04684 mol\text{moles of naphthalene} = \frac{6.000 \, \text{g}}{128.18 \, \text{g/mol}} = 0.04684 \, \text{mol}moles of naphthalene=128.18g/mol6.000g=0.04684mol
Step 2: Convert moles to molecules
Next, we use Avogadro’s number to convert moles to molecules. Avogadro’s number is 6.022×10236.022 \times 10^{23}6.022×1023 molecules per mole. To find the number of molecules in 0.04684 moles of naphthalene, we multiply the moles by Avogadro’s number:number of molecules=0.04684 mol×6.022×1023 molecules/mol\text{number of molecules} = 0.04684 \, \text{mol} \times 6.022 \times 10^{23} \, \text{molecules/mol}number of molecules=0.04684mol×6.022×1023molecules/molnumber of molecules=2.82×1022 molecules\text{number of molecules} = 2.82 \times 10^{22} \, \text{molecules}number of molecules=2.82×1022molecules
Final Answer:
So, the number of molecules of naphthalene in a 6.000 g mothball is approximately 2.82×10222.82 \times 10^{22}2.82×1022 molecules.
This process shows how to go from mass to moles and then to molecules, using the molar mass of naphthalene and Avogadro’s number.
