Calculate the number of atoms that are present in 98.5 grams of gold.
Understand the Problem
The question is asking us to calculate the number of atoms in a given mass of gold (98.5 grams). To solve this, we can use Avogadro's number and the molar mass of gold.
Answer
$3.011 \times 10^{23}$ atoms
Answer for screen readers
The number of atoms in 98.5 grams of gold is approximately $3.011 \times 10^{23}$ atoms.
Steps to Solve
- Determine the molar mass of gold
The molar mass of gold (Au) is approximately 197 g/mol. This means that one mole of gold has a mass of 197 grams.
- Calculate the number of moles of gold in 98.5 grams
To find the number of moles of gold in 98.5 grams, use the formula:
$$ \text{Number of moles} = \frac{\text{mass}}{\text{molar mass}} $$
Substituting the known values:
$$ \text{Number of moles} = \frac{98.5 \text{ g}}{197 \text{ g/mol}} \approx 0.500 \text{ moles} $$
- Use Avogadro's number to find the number of atoms
Now, we use Avogadro's number, which is approximately $6.022 \times 10^{23}$ atoms/mol, to convert moles to atoms:
$$ \text{Number of atoms} = \text{Number of moles} \times \text{Avogadro's number} $$
Calculating the total number of atoms:
$$ \text{Number of atoms} = 0.500 \text{ moles} \times 6.022 \times 10^{23} \text{ atoms/mol} \approx 3.011 \times 10^{23} \text{ atoms} $$
The number of atoms in 98.5 grams of gold is approximately $3.011 \times 10^{23}$ atoms.
More Information
This calculation uses fundamental concepts from chemistry, specifically the relationship between mass, moles, and the number of atoms. Understanding Avogadro's number is crucial for converting between these quantities.
Tips
- Forgetting to convert grams to moles by using the molar mass.
- Misapplying Avogadro's number, either by using the wrong value or miscalculating the final number of atoms.
- Not paying attention to significant figures; ensure your final answer reflects the appropriate number of significant digits based on the values used.
