A tank holds 2.85 L of oxygen at 22.1 Celsius and 235 atm. (A) how many moles of gas does the tank contain? (B) what is the average kinetic energy per molecule ?
(A) (2.85/22.4)* 235*(273.2/295.3) moles
(B) (3/2)kT
k is the Boltzmann constant.
If you include kinetic energy of O2 molecule rotation, the answer is (5/2) kT
but the answer in the text book is (a) 27.7 moles (b) 2.381x10^7pa
i just want the formula so i can attempt the problem myself
My answer to (A) agrees with the text book.
The answer to (B) cannot be in Pascals. You mistyped something or the book is wrong. I gave you the formula.
If u type this question in to the google it will give u the answer which agrees with your text book
What is k in the formula (3/2)kT
To answer these questions, we'll need to use the ideal gas law and the formula for average kinetic energy.
(A) To find the number of moles of gas, we can use the ideal gas law, which is expressed as:
PV = nRT
Where:
P is the pressure of the gas (in atm).
V is the volume of the gas (in L).
n is the number of moles of gas.
R is the ideal gas constant (0.0821 L·atm/mol·K).
T is the temperature of the gas (in Kelvin).
First, we need to convert the given temperature from Celsius to Kelvin. To do this, add 273.15 to the Celsius temperature:
22.1 °C + 273.15 = 295.25 K
Next, we can substitute the given values into the ideal gas law equation:
(235 atm) * (2.85 L) = n * (0.0821 L·atm/mol·K) * (295.25 K)
Simplifying the equation:
669.75 atm·L = 24.17145n
Now, isolate n by dividing both sides by 24.17145:
n = (669.75 atm·L) / (24.17145)
Calculate n:
n ≈ 27.7 moles
Therefore, the tank contains approximately 27.7 moles of gas.
(B) To find the average kinetic energy per molecule, we can use the formula for average kinetic energy:
KE_avg = (3/2) * (k * T)
Where:
KE_avg is the average kinetic energy per molecule.
k is the Boltzmann constant (1.38 × 10^-23 J/K).
T is the temperature of the gas (in Kelvin).
First, convert the given temperature from Celsius to Kelvin as previously explained:
22.1 °C + 273.15 = 295.25 K
Next, substitute the values into the formula for average kinetic energy:
KE_avg = (3/2) * (1.38 × 10^-23 J/K) * (295.25 K)
Calculating the expression:
KE_avg ≈ 6.41 × 10^-21 J
Therefore, the average kinetic energy per molecule is approximately 6.41 × 10^-21 J.