Sure! Let's solve the problem step-by-step.
1. Understand the Given Data:
- We have 2.0 moles of [tex]\( CO_2 \)[/tex].
- Avogadro's number states that 1 mole of any substance contains [tex]\( 6.02 \times 10^{23} \)[/tex] particles (molecules in this case).
2. Calculate the Number of Molecules:
To find the total number of molecules in 2.0 moles of [tex]\( CO_2 \)[/tex], we 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:
Multiply the coefficients (2.0 and 6.02):
[tex]\[
2.0 \times 6.02 = 12.04
\][/tex]
Now, according to the rules of scientific notation, we still have [tex]\( 10^{23} \)[/tex] as the exponent. So:
[tex]\[
\text{Number of molecules} = 12.04 \times 10^{23}
\][/tex]
4. Adjust the Scientific Notation:
Here, the coefficient (12.04) falls within the acceptable range for scientific notation (1 to 10). However, since typically we express coefficients as an integer, we can round 12.04 to 12.
5. Final Answer:
Therefore, the approximate number of molecules in 2.0 moles of [tex]\( CO_2 \)[/tex] is:
[tex]\[
12 \times 10^{23} \, \text{molecules of } CO_2
\][/tex]
So, you should fill in:
- The green box with the coefficient [tex]\( \mathbf{12} \)[/tex],
- The yellow box with the exponent [tex]\( \mathbf{23} \)[/tex].
