To determine the number of molecules in 2.0 moles of [tex]\( \text{CO}_2 \)[/tex], we can use Avogadro's number. Avogadro's number is [tex]\( 6.02 \times 10^{23} \)[/tex] particles per mole. This constant allows us to convert moles of a substance directly into the number of particles (molecules in this case).
Here is the detailed step-by-step calculation:
1. Identify the given data:
- Number of moles of [tex]\( \text{CO}_2 \)[/tex]: [tex]\( 2.0 \)[/tex] moles
- Avogadro's number: [tex]\( 6.02 \times 10^{23} \)[/tex] particles/mole
2. Calculate the number of molecules:
To find the number of molecules in [tex]\( 2.0 \)[/tex] moles of [tex]\( \text{CO}_2 \)[/tex], multiply the number of moles by Avogadro's number:
[tex]\[
\text{Number of molecules} = 2.0 \, \text{moles} \times 6.02 \times 10^{23} \, \text{molecules/mole}
\][/tex]
3. Perform the multiplication:
[tex]\[
\text{Number of molecules} = 2.0 \times 6.02 \times 10^{23}
\][/tex]
Multiplying the coefficients:
[tex]\[
2.0 \times 6.02 = 12.04
\][/tex]
Keep the exponent the same:
[tex]\[
12.04 \times 10^{23}
\][/tex]
4. Conclusion:
The number of molecules in 2.0 moles of [tex]\( \text{CO}_2 \)[/tex] is:
[tex]\[
12.04 \times 10^{23} \, \text{molecules}
\][/tex]
In conclusion, [tex]\( \boxed{12.04} \)[/tex] is the coefficient, and [tex]\( \boxed{23} \)[/tex] is the exponent for the number of molecules of [tex]\( \text{CO}_2 \)[/tex].
