To determine the number of moles of nitrogen gas ([tex]\(N_2\)[/tex]), we are given:
- The mass of the nitrogen gas ([tex]\(N_2\)[/tex]) is 86 grams.
- The molar mass of [tex]\(N_2\)[/tex] is 28 grams per mole.
We can use the relationship for calculating the number of moles:
[tex]\[
\text{Number of moles} = \frac{\text{Mass of substance}}{\text{Molar mass of substance}}
\][/tex]
Substitute the given values into the equation:
[tex]\[
\text{Number of moles of } N_2 = \frac{86 \text{ grams}}{28 \text{ grams per mole}}
\][/tex]
Perform the division:
[tex]\[
\text{Number of moles of } N_2 = \frac{86}{28} \approx 3.0714285714285716
\][/tex]
To express this value to three decimal places:
[tex]\[
\text{Number of moles of } N_2 \approx 3.071
\][/tex]
Therefore, the number of moles of nitrogen gas ([tex]\(N_2\)[/tex]) when rounded to three decimal places is:
[tex]\[
3.071 \text{ mol}
\][/tex]
