A nine liter tank has 150 atmospheres of bromine in it at 27°C. What is the added mass of the tank due to the gas?
Use PV = nRT and solve for n = number of mols. Then n = grams/molar mass. You know n and molar mass, solve for grams.
To calculate the added mass of the tank due to the gas, we need to consider the ideal gas law and the molar mass of bromine.
The ideal gas law equation is:
PV = nRT
Where:
P = Pressure (in atmospheres)
V = Volume (in liters)
n = Number of moles
R = Ideal gas constant
T = Temperature (in Kelvin)
First, let's convert the temperature from Celsius to Kelvin. The Kelvin temperature is obtained by adding 273.15 to the Celsius temperature.
T = 27°C + 273.15 = 300.15K
Now we have the following information:
P = 150 atmospheres
V = 9 liters
R = 0.0821 liter·atm/mol·K (ideal gas constant for atm units)
We need to find n (the number of moles). Rearranging the ideal gas law equation gives us:
n = PV / RT
n = (150 atm * 9 L) / (0.0821 L·atm/mol·K * 300.15 K)
n = 49.24 moles
Next, we need to find the molar mass of bromine (Br₂). The molar mass of bromine is about 79.9 g/mol.
Finally, we can calculate the added mass of the tank due to the gas by multiplying the number of moles by the molar mass:
Added mass of the tank (in grams) = n (moles) * molar mass (g/mol)
Added mass of the tank = 49.24 moles * 79.9 g/mol
Added mass of the tank ≈ 3,933.476g
Therefore, the added mass of the tank due to the gas is approximately 3,933.476 grams.