Answer :
Certainly! To determine which has more atoms between [tex]\( \frac{1}{2} \)[/tex] mole of gold (Au) and 1 mole of sodium (Na), we can follow these steps:
### Step 1: Understanding the Concept of a Mole
A mole is a unit that measures the amount of a substance. One mole of any substance contains [tex]\( 6.022 \times 10^{23} \)[/tex] entities (atoms, molecules, ions, etc.), which is known as Avogadro's number.
### Step 2: Calculating the Number of Atoms
Let's calculate the number of atoms in each of the given quantities.
#### For [tex]\( \frac{1}{2} \)[/tex] mole of Au:
- Moles of Au: [tex]\( \frac{1}{2} = 0.5 \)[/tex] mole
- Number of Atoms in [tex]\( \frac{1}{2} \)[/tex] mole of Au:
[tex]\[ 0.5 \, \text{mole} \times 6.022 \times 10^{23} \, \text{atoms/mole} = 3.011 \times 10^{23} \, \text{atoms} \][/tex]
#### For 1 mole of Na:
- Moles of Na: [tex]\( 1 \)[/tex] mole
- Number of Atoms in 1 mole of Na:
[tex]\[ 1 \, \text{mole} \times 6.022 \times 10^{23} \, \text{atoms/mole} = 6.022 \times 10^{23} \, \text{atoms} \][/tex]
### Step 3: Comparing the Number of Atoms
Now, let's compare the number of atoms calculated for Au and Na.
- [tex]\( \text{Number of Atoms in } \frac{1}{2} \text{ mole of Au} = 3.011 \times 10^{23} \, \text{atoms} \)[/tex]
- [tex]\( \text{Number of Atoms in } 1 \text{ mole of Na} = 6.022 \times 10^{23} \, \text{atoms} \)[/tex]
Clearly:
[tex]\[ 6.022 \times 10^{23} \, \text{atoms} > 3.011 \times 10^{23} \, \text{atoms} \][/tex]
### Conclusion
1 mole of sodium (Na) has more atoms than [tex]\( \frac{1}{2} \)[/tex] mole of gold (Au).
So, 1 mole of Na has more atoms.
### Step 1: Understanding the Concept of a Mole
A mole is a unit that measures the amount of a substance. One mole of any substance contains [tex]\( 6.022 \times 10^{23} \)[/tex] entities (atoms, molecules, ions, etc.), which is known as Avogadro's number.
### Step 2: Calculating the Number of Atoms
Let's calculate the number of atoms in each of the given quantities.
#### For [tex]\( \frac{1}{2} \)[/tex] mole of Au:
- Moles of Au: [tex]\( \frac{1}{2} = 0.5 \)[/tex] mole
- Number of Atoms in [tex]\( \frac{1}{2} \)[/tex] mole of Au:
[tex]\[ 0.5 \, \text{mole} \times 6.022 \times 10^{23} \, \text{atoms/mole} = 3.011 \times 10^{23} \, \text{atoms} \][/tex]
#### For 1 mole of Na:
- Moles of Na: [tex]\( 1 \)[/tex] mole
- Number of Atoms in 1 mole of Na:
[tex]\[ 1 \, \text{mole} \times 6.022 \times 10^{23} \, \text{atoms/mole} = 6.022 \times 10^{23} \, \text{atoms} \][/tex]
### Step 3: Comparing the Number of Atoms
Now, let's compare the number of atoms calculated for Au and Na.
- [tex]\( \text{Number of Atoms in } \frac{1}{2} \text{ mole of Au} = 3.011 \times 10^{23} \, \text{atoms} \)[/tex]
- [tex]\( \text{Number of Atoms in } 1 \text{ mole of Na} = 6.022 \times 10^{23} \, \text{atoms} \)[/tex]
Clearly:
[tex]\[ 6.022 \times 10^{23} \, \text{atoms} > 3.011 \times 10^{23} \, \text{atoms} \][/tex]
### Conclusion
1 mole of sodium (Na) has more atoms than [tex]\( \frac{1}{2} \)[/tex] mole of gold (Au).
So, 1 mole of Na has more atoms.
