Answer :

Sure, let's go through the steps to solve this problem:

1. Identify the given information:
- Volume of the tank ([tex]\(V\)[/tex]): 6.00 liters
- Mass of nitrogen gas ([tex]\(\text{mass}\)[/tex]): 21.4 grams
- Temperature ([tex]\(T\)[/tex]): 385 Kelvin
- Molar mass of nitrogen ([tex]\(\text{molar mass}\)[/tex]): 28.02 g/mol (since nitrogen gas is diatomic, [tex]\(\text{N}_2\)[/tex])

2. Calculate the number of moles of nitrogen ([tex]\(n\)[/tex]):
To find the number of moles, use the formula:
[tex]\[
n = \frac{\text{mass}}{\text{molar mass}}
\][/tex]
Substituting the given values:
[tex]\[
n = \frac{21.4 \, \text{g}}{28.02 \, \text{g/mol}} \approx 0.7637 \, \text{mol}
\][/tex]

3. Use the ideal gas law to find the pressure ([tex]\(P\)[/tex]):
The ideal gas law is given by:
[tex]\[
PV = nRT
\][/tex]
Solve for pressure ([tex]\(P\)[/tex]):
[tex]\[
P = \frac{nRT}{V}
\][/tex]
Where the ideal gas constant ([tex]\(R\)[/tex]) is 0.0821 L atm / (mol K).

4. Substitute the known values into the equation:
[tex]\[
P = \frac{0.7637 \, \text{mol} \times 0.0821 \, \text{L atm / (mol K)} \times 385 \, \text{K}}{6.00 \, \text{L}}
\][/tex]
[tex]\[
P \approx 4.023 \, \text{atm}
\][/tex]

So, the pressure in the tank is approximately 4.023 atm.

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Rewritten by : Barada