Sure, let's find out the volume occupied by 4.4 grams of [tex]\(CO_2\)[/tex] at Standard Temperature and Pressure (STP). Here are the steps to solve this problem:
1. Calculate the number of moles of [tex]\(CO_2\)[/tex]:
First, we need to find out how many moles of [tex]\(CO_2\)[/tex] are present in 4.4 grams. We know the molar mass of [tex]\(CO_2\)[/tex] (carbon dioxide) is 44.01 g/mol.
The formula to find the number of moles ([tex]\(n\)[/tex]) is:
[tex]\[
n = \frac{\text{mass}}{\text{molar mass}}
\][/tex]
Substituting the given values:
[tex]\[
n = \frac{4.4 \text{ grams}}{44.01 \text{ g/mol}}
\][/tex]
2. Perform the division to find the moles:
After calculating the division, we get:
[tex]\[
n = 0.09997727789138833 \text{ moles}
\][/tex]
3. Calculate the volume occupied at STP:
At Standard Temperature and Pressure (STP), one mole of any gas occupies 22.414 liters. We use this property to find the volume that our calculated moles of [tex]\(CO_2\)[/tex] will occupy.
The formula to find the volume ([tex]\(V\)[/tex]) is:
[tex]\[
V = n \times 22.414 \text{ liters/mole}
\][/tex]
Substituting the number of moles we found:
[tex]\[
V = 0.09997727789138833 \times 22.414
\][/tex]
4. Perform the multiplication to find the volume:
After performing the multiplication, we get:
[tex]\[
V = 2.240890706657578 \text{ liters}
\][/tex]
Therefore, the volume occupied by 4.4 grams of [tex]\(CO_2\)[/tex] at STP is [tex]\(2.240890706657578\)[/tex] liters.
