You have a metal tank containing 74.0 moles of nitrogen gas at a pressure of 15.0 atm. If the pressure is measured at a temperature of 25.0 °C, then the volume of the tank must be ___ liters
Use PV = nRT. Remember T must be in kelvin. V will be in L.
To determine the volume of the tank, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure (in atm)
V = volume (in liters)
n = number of moles
R = ideal gas constant (0.0821 L·atm/mol·K)
T = temperature (in Kelvin)
First, we need to convert the given temperature from Celsius to Kelvin:
T(K) = T(°C) + 273.15
T(K) = 25.0 °C + 273.15 = 298.15 K
Now, we can substitute the given values into the ideal gas law equation:
(15.0 atm) • V = (74.0 moles) • (0.0821 L·atm/mol·K) • (298.15 K)
Simplifying the equation:
15.0V = 18.873 L·atm
To find the volume (V), divide both sides of the equation by 15.0:
V = 18.873 L·atm / 15.0
V ≈ 1.258 L
Therefore, the approximate volume of the tank is 1.258 liters.