4 moles CO, 5 moles N2 and 2 moles C2H4 are placed in a 5 liter vessel at 27 degree celsius . the ratio of kinetic energy per molecule of CO2, He and NH3 is
To find the ratio of kinetic energy per molecule of CO2, He, and NH3, we need to calculate the kinetic energy of each gas molecule and then compare them.
The kinetic energy of a gas molecule can be calculated using the formula:
KE = (3/2) * k * T
where KE is the kinetic energy, k is the Boltzmann constant (1.38 x 10^-23 J/K), and T is the temperature in Kelvin.
Let's calculate the number of molecules for each gas using the ideal gas equation:
PV = nRT
where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant (0.0821 L·atm/(mol·K)), and T is the temperature in Kelvin.
For CO2:
PV = nRT
Assuming pressure is constant at standard atmospheric pressure (1 atm)
(1 atm) * (5 L) = (n CO2) * (0.0821 L·atm/(mol·K)) * (27 + 273 K)
n CO2 = (5/0.0821) * (27 + 273)
n CO2 = 166.21 moles
For He:
PV = nRT
Assuming pressure is constant at standard atmospheric pressure (1 atm)
(1 atm) * (5 L) = (n He) * (0.0821 L·atm/(mol·K)) * (27 + 273 K)
n He = (5/0.0821) * (27 + 273)
n He = 166.21 moles
For NH3:
PV = nRT
Assuming pressure is constant at standard atmospheric pressure (1 atm)
(1 atm) * (5 L) = (n NH3) * (0.0821 L·atm/(mol·K)) * (27 + 273 K)
n NH3 = (5/0.0821) * (27 + 273)
n NH3 = 166.21 moles
Now that we have the number of molecules for each gas, we can calculate the kinetic energy per molecule.
For CO2:
KE CO2 = (3/2) * (1.38 x 10^-23 J/K) * (27 + 273) K
KE CO2 = 4.14 x 10^-23 J
For He:
KE He = (3/2) * (1.38 x 10^-23 J/K) * (27 + 273) K
KE He = 4.14 x 10^-23 J
For NH3:
KE NH3 = (3/2) * (1.38 x 10^-23 J/K) * (27 + 273) K
KE NH3 = 4.14 x 10^-23 J
Therefore, the ratio of kinetic energy per molecule of CO2, He, and NH3 is 1:1:1.