Determine the pressure in a 125-L tank containing 56.2 kg of oxygen gas at 25 °C.
So, PV=nRT
I convert 25 °C to 298.15 K
Do I have to convert anything else?
What else do I do?
Convert 56.2 kg oxygen to moles = n.
n = grams (not kg)/molar mass.
Yes, converting temperature to Kelvin is correct. In addition to that, you need to convert the mass of oxygen gas to moles by using the molar mass of oxygen.
1. Determine the molar mass of oxygen (O2).
The molar mass of oxygen is 32 g/mol.
2. Calculate the number of moles (n) of oxygen gas.
n = mass / molar mass
n = 56.2 kg / (32 g/mol)
Note: Be sure to convert the mass from kg to g to match the molar mass unit.
n = 56,200 g / (32 g/mol)
3. Substitute the values in the ideal gas law equation, PV = nRT.
P * V = n * R * T
Given:
V = 125 L
T = 298.15 K (25 °C converted to Kelvin)
R = 0.0821 L·atm/mol·K (gas constant)
P * 125 L = (56,200 g / 32 g/mol) * (0.0821 L·atm/mol·K) * 298.15 K
4. Calculate the pressure (P) by rearranging the equation:
P = (n * R * T) / V
P = (56,200 g / 32 g/mol) * (0.0821 L·atm/mol·K) * 298.15 K / 125 L
Now, you can proceed to perform the calculations to determine the pressure in the tank.
To determine the pressure in the tank, you need to rearrange the ideal gas law equation (PV = nRT) to solve for pressure (P). Here's how you can proceed:
1. Convert the temperature from Celsius to Kelvin. As you correctly mentioned, 25 °C is equivalent to 298.15 K. This step ensures that the temperature is in the correct SI unit for calculations.
2. Calculate the number of moles of oxygen gas (n). To do this, you need to know the molar mass of oxygen (O₂). The molar mass is 32 g/mol. Convert the mass of oxygen gas in the tank (56.2 kg) to grams by multiplying it by 1000. Then, divide the mass by the molar mass to find the number of moles.
Number of moles (n) = (mass of oxygen gas in g) / (molar mass of oxygen)
3. Substitute the known values into the ideal gas law equation and solve for pressure (P).
P * V = n * R * T
Plug the values into the equation:
Pressure (P) = (number of moles (n) * gas constant (R) * temperature (T)) / volume (V)
The gas constant (R) is a constant value of 8.314 J/(mol*K).
4. Convert the volume from liters (L) to cubic meters (m³). The conversion factor is 1 L = 0.001 m³.
Volume (V) = 125 L * 0.001 m³/L
5. Finally, substitute the determined values into the equation to calculate the pressure in units of pascals (Pa). 1 Pa = 1 N/m².
Pressure (P) = ((number of moles (n) * gas constant (R) * temperature (T)) / volume (V)) in pascals
Follow these steps to find the pressure in the 125-L tank containing 56.2 kg of oxygen gas at 25 °C.