To find the temperature in degrees Celsius, 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 pressure from Torr to atm. Since 1 atm = 760 Torr, we divide 6177 Torr by 760 to get the pressure in atm:
6177 Torr ÷ 760 Torr/atm = 8.125 atm
Next, we need to calculate the number of moles of H2 gas:
n = mass / molar mass
n = 13.57 g / 2.016 g/mol = 6.73 mol
Now, we can rearrange the ideal gas law equation to solve for temperature:
T = PV / nR
T = (8.125 atm) x (7.00 L) / (6.73 mol) x (0.0821 L·atm/mol·K)
T ≈ 76.9 K
To convert the temperature to degrees Celsius, we subtract 273.15:
T = 76.9 K - 273.15 = -196.25 °C
Therefore, the temperature of the 7.00 L tank containing 13.57 g of H2 gas, assuming ideal behavior, is approximately -196.25 °C.