What is the pressure in a 5.00 L tank with 7.90 moles of oxygen at 39.3 °C?

Sure! To find the pressure in a 5.00 L tank with 7.90 moles of oxygen at 39.3 °C, we can use the Ideal Gas Law, which is given by the formula:

[tex]\[ PV = nRT \][/tex]

Where:
- [tex]$ P $[/tex] is the pressure in atmospheres
- [tex]$ V $[/tex] is the volume in liters
- [tex]$ n $[/tex] is the number of moles of the gas
- [tex]$ R $[/tex] is the Ideal Gas Constant, which is 0.0821 L atm/mol K
- [tex]$ T $[/tex] is the temperature in Kelvin

Here are the steps to solve the problem:

1. Convert the Temperature to Kelvin:
The given temperature is 39.3 °C. To convert degrees Celsius to Kelvin, you add 273.15:
[tex]\[ T = 39.3 + 273.15 = 312.45 \, \text{K} \][/tex]

2. Apply the Ideal Gas Law:
We know the following values:
- [tex]$ n = 7.90 $[/tex] moles
- [tex]$ V = 5.00 $[/tex] L
- [tex]$ R = 0.0821 $[/tex] L atm/mol K
- [tex]$ T = 312.45 $[/tex] K

Substituting these values into the formula [tex]$ PV = nRT $[/tex] and solving for [tex]$ P $[/tex]:

[tex]\[ P = \frac{nRT}{V} \][/tex]

[tex]\[ P = \frac{7.90 \times 0.0821 \times 312.45}{5.00} \][/tex]

3. Calculate the Pressure:
Compute the pressure [tex]$ P $[/tex]:

[tex]\[ P \approx 40.53 \, \text{atm} \][/tex]

So, the pressure in the tank is approximately 40.53 atm.