How much volume in liters will 100.0 g of oxygen occupy at 100 degrees celcius and 100 atm pressure?
100 C = 373 K and 100 g of O2 is 100/32 = 3.125 moles.
You could use the formula V = nRT/P directly (if you know R), or reason as follows:
At STP (0 C and 1 atm), that amount of O2 would occupy 3.125 moles x 22.4 (l/mole) = 70.0 liters
Finally, multiply that by (373/273)(1/100) to get the volume at 100 atm and 100 C
To calculate the volume of a gas, 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)
To solve for V, we need to convert the given temperature from degrees Celsius to Kelvin:
T(K) = T(°C) + 273.15
So, let's now solve the problem step by step:
Step 1: Convert the temperature from Celsius to Kelvin:
T(K) = 100°C + 273.15 = 373.15 K
Step 2: Use the ideal gas law to find the number of moles of oxygen:
PV = nRT
n = PV / RT
Given:
P = 100 atm
V = ?
n = ?
R = 0.0821 L.atm/mol.K
T = 373.15 K
We need to first convert the given mass of oxygen to moles using its molar mass.
Step 3: Calculate the number of moles of oxygen:
Molar mass of oxygen (O2) = 32.00 g/mol
Given:
Mass of oxygen (m) = 100.0 g
Molar mass (M) = 32.00 g/mol
n = m / M
n = 100.0 g / 32.00 g/mol
Step 4: Calculate the volume using the ideal gas law equation:
V = nRT / P
V = (100.0 g / 32.00 g/mol) * (0.0821 L.atm/mol.K) * (373.15 K) / 100 atm
Now, we can calculate the volume in liters.
Solution:
Substituting the given values into the equation:
V = (100.0 g / 32.00 g/mol) * (0.0821 L.atm/mol.K) * (373.15 K) / 100 atm
V ≈ 96.79 liters
Therefore, 100.0 g of oxygen will occupy approximately 96.79 liters at 100 degrees Celsius and 100 atm pressure.