Three moles of oxygen gas (O2) are placed in a portable container with a volume of 0.0037 m3. The temperature of the gas is 330°C.
(a) What is the pressure of the gas?
? Pa
(b) What is the average kinetic energy of an oxygen molecule?
? J
a) Use the ideal gas law to find pressure
PV=nRT
b) avgKE= 5/2 k T where the 5/2 is used for diatomic gases, and k is Bultmann's constant.
To find the pressure of the gas, we can use the ideal gas law equation:
PV = nRT,
where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature in Kelvin.
To find the pressure, we need to convert the temperature from Celsius to Kelvin:
T(K) = T(°C) + 273.15
T(K) = 330 + 273.15
T(K) = 603.15 K
Now we can plug in the values into the ideal gas law equation:
P * 0.0037 = 3 * R * 603.15
To find the pressure in Pascal (Pa), we need to know the value of the gas constant, R. The value of R depends on the units used for pressure and volume.
For pressure in Pascal (Pa) and volume in cubic meters (m3), the value of R is 8.314 J/(mol·K).
(a) Plugging in the values:
P * 0.0037 = 3 * 8.314 * 603.15
P = (3 * 8.314 * 603.15) / 0.0037
P ≈ 316,970 Pa
Therefore, the pressure of the gas is approximately 316,970 Pa.
To find the average kinetic energy of an oxygen molecule, we can use the equation:
KE = (3/2) * k * T,
where KE is the kinetic energy, k is the Boltzmann constant, and T is the temperature in Kelvin.
The value of the Boltzmann constant, k, is approximately 1.38 × 10^-23 J/K.
(b) Plugging in the values:
KE = (3/2) * 1.38 × 10^-23 * 603.15
KE ≈ 1.986 × 10^-21 J
Therefore, the average kinetic energy of an oxygen molecule is approximately 1.986 × 10^-21 J.
To find the pressure of the gas, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure of the gas (in Pa)
V = volume of the gas (in m^3)
n = number of moles of the gas
R = ideal gas constant (8.314 J/(mol·K))
T = temperature of the gas (in K)
First, let's convert the temperature from Celsius to Kelvin:
T(K) = T(°C) + 273.15
So, T(K) = 330 + 273.15 = 603.15 K
Now, we can substitute the known values into the ideal gas law equation:
P * 0.0037 = 3 * 8.314 * 603.15
Simplifying the equation:
P = (3 * 8.314 * 603.15) / 0.0037
Calculating the pressure:
P ≈ 404,799.2 Pa
Therefore, the pressure of the gas is approximately 404,799.2 Pa.
To find the average kinetic energy of an oxygen molecule, we can use the kinetic theory of gases. The average kinetic energy (KE) of a gas molecule can be calculated using the following equation:
KE = (3/2) * (k * T)
Where:
k = Boltzmann constant (1.38 x 10^-23 J/K)
T = temperature of the gas (in K)
Substituting the known values:
KE = (3/2) * (1.38 x 10^-23 J/K * 603.15 K)
Simplifying the equation:
KE ≈ 1.65 x 10^-21 J
Therefore, the average kinetic energy of an oxygen molecule is approximately 1.65 x 10^-21 J.