Review Problem 4. a) The approximate dimensions of our classroom are 8.0 m x 8.0

Question

Review Problem 4. a) The approximate dimensions of our classroom are 8.0 m x 8.0 m x 3.0 m. The total air pressure is 8.4 x 104 Pa and the temperature is 22°C. If the partial pressure of oxygen is 21% of the total pressure, how many moles of oxygen are there in the room? b) What is the total mass of oxygen in the room? c) Under these conditions, what is the root mean square speed of the oxygen molecules? d) Using the principle of the equipartition of energy, and the value for the molar heat capacity of N2, determine the number of degrees of freedom of the nitrogen molecule. Is it necessary to include vibrational motion to account for this value?

Explanation / Answer

The volume of the room is 8m X 8 m X 3 m = 192 m^3

The volume of the room in L =192 m^3 X 1000 L/m^3 = 19.2X10^4 L

Now, at STP, 1 mole of any gas occupies a volume of 22.4 L. So, the moles of gas in the room is:

19.2X10^4 L X 1 mol/22.4L = 8571.4 moles. Since O2 makes up 21% of air,

8571.4 mol X 0.21 = 1800 moles O2

2.Mass O2 = 1800 moles X 32 g/mol = 5.76X10^4 grams O2 in the room

3.

AT 293K

vrms = ?{(3RT)/M} = ?{(3*8.3145*293)/0.032} = 477.9 or 478 m/s

4.The kinetic energy of a gas will be equal to:

3/2 kT, where k = Boltzmann's constant = 1.38x10^-23 J/K and T is the temperature.

At room temperature the kinetic energy will be:

E = 3/2(1.38x10^-23 J/K)(298.15 K) = 6.17x10^-21 J.

Related Questions

Navigate

• Browse (All)
• Browse R
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.