Answer :
The pressure in the tank is 3.793 atmospheres.
The pressure in the tank is calculated using the ideal gas law, which is given by PV = nRT, where P is the pressure, V is the volume, n is the number of moles of the gas, R is the ideal gas constant, and T is the temperature in Kelvin.
First, we need to calculate the number of moles (n) of nitrogen gas (N₂) present in the tank. The molar mass of nitrogen gas is 28.02 g/mol (14.01 g/mol for nitrogen multiplied by 2, since N₂ has two nitrogen atoms). Using the given mass of nitrogen gas (20.0 g), we can find the number of moles as follows:
[tex]\[ n = \frac{\text{mass}}{\text{molar mass}} = \frac{20.0 \text{ g}}{28.02 \text{ g/mol}} \approx 0.714 \text{ mol} \][/tex]
Next, we have the volume V = 6.00 L, the ideal gas constant R = 0.0821 L·atm/(mol·K), and the temperature T = 385 K.
Now, we can rearrange the ideal gas law to solve for the pressure P:
[tex]\[ P = \frac{nRT}{V} \][/tex]
Plugging in the values:
[tex]\[ P = \frac{(0.714 \text{ mol})(0.0821 \text{ Latm/(mol~K)})(385 \text{ K})}{6.00 \text{ L}} \] \[ P = \frac{(0.714)(0.0821)(385)}{6.00} \] \[ P \approx \frac{22.76}{6.00} \] \[ P \approx 3.793 \text{ atm} \][/tex]
Therefore, the pressure in the tank is approximately 3.793 atmospheres.
