Some oxygen gas has a volume of 41.0 L under a pressure of 245 kPa and a temperature of 279 K. What is the mass of the gas?
To find the mass of the gas, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure (in Pascal)
V = volume (in cubic meters)
n = number of moles of gas
R = ideal gas constant (8.314 J/(mol*K))
T = temperature (in Kelvin)
First, we need to convert the given values to the appropriate units.
Pressure:
1 kPa = 1000 Pa
So, the pressure is 245 kPa * 1000 = 245000 Pa
Volume:
1 L = 0.001 m^3
So, the volume is 41.0 L * 0.001 = 0.041 m^3
Temperature:
Given as 279 K
Now, we can rearrange the equation to solve for the number of moles:
n = (PV) / (RT)
Substituting the values:
n = (245000 Pa * 0.041 m^3) / (8.314 J/(mol*K) * 279 K)
Simplifying:
n = 3.0383 moles
The molar mass of oxygen (O2) is approximately 32 g/mol. Therefore, we can calculate the mass of the gas:
mass = n * molar mass
mass = 3.0383 moles * 32 g/mol
mass = 97.0986 grams
Therefore, the mass of the gas is approximately 97.1 grams.
To find the mass of the gas, you need to use the ideal gas law equation which is:
PV = nRT
where:
P = pressure of the gas (in kilopascals, kPa)
V = volume of the gas (in liters, L)
n = number of moles of gas
R = ideal gas constant (8.314 J/(mol·K))
T = temperature of the gas (in Kelvin, K)
First, let's convert the pressure from kilopascals to pascals (Pa) by multiplying by 1000:
245 kPa * 1000 = 245,000 Pa
Next, convert the volume from liters to cubic meters (m^3) by multiplying by 0.001:
41.0 L * 0.001 = 0.041 m^3
Now, let's rearrange the ideal gas law equation to solve for the number of moles (n):
n = PV / RT
Plug in the given values:
n = (245,000 Pa) * (0.041 m^3) / ((8.314 J/(mol·K)) * (279 K))
Perform the calculation:
n ≈ 34.57 moles
Finally, to find the mass, you need to know the molar mass of oxygen (O₂) which is approximately 32.00 g/mol. Multiply the number of moles by the molar mass:
mass = n * molar mass
mass ≈ 34.57 moles * (32.00 g/mol)
mass ≈ 1,105.44 g
Therefore, the mass of the oxygen gas is approximately 1,105.44 grams.
PV = nRT
I would change 245 kPa to atmospheres. Then plug in V, R, and T (already in Kelvin), and solve for n = number of moles. Then number moles = grams/molar mass. You know moles and molar mass. Calculate grams.