Kinetic Theory of Gases and speed of oxygen molecules

In summary, the question asks for the root mean square speed of oxygen molecules in a syringe that has been used and is now empty on a doctor's desk, when the number of oxygen molecules is 6.5 x 1019, the pressure is 100,000 Pa, and the volume and percentage of oxygen remain the same. Using the kinetic theory of gas and the given values for temperature, molar mass of oxygen, and gas constant, the root mean square speed can be calculated to be 6.13 m/s. However, it is important to note that the incorrect value for mass was initially used in the calculation, which resulted in the wrong answer. The correct mass should be 0.032 kg/mol divided by
  • #1
cyberdx16
16
0

Homework Statement



A syringe of volume 20 ml has just been used and now lies empty on the doctor's desk. The pressure in the office is 100,000 Pa. Assume that the air is an ideal gas consisting of nitrogen N2 (80%) and oxygen O2 (20%) molecules. k=1.38×10-23 J/K and the molar mass of oxygen is 32 g/mol.

The syringe must be heated to high temperatures to sterilize it. When the syringe is at its maximum temperature, the number of oxygen molecules is 6.5 x 1019 (but the pressure, volume, and percent oxygen remain the same), what is the rms speed of the oxygen molecules?

Homework Equations



Kinetic theory of Gas

KE=m(v^2)/2=3KT/2

The Attempt at a Solution

m=32/6.5e19=4.9e-22kgNot sure if this is right..
k=1.38e-23
T=445.93

v=sq rt(3(1.38e-23)(445.93)/4.9e-22)

so i got 6.13m/s but its wrong, can someone explain to me what i did wrong?
 
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  • #2
figured it out, mass should of been .032Kg/6.022e23
 
  • #3


Your approach and equations are correct, but there is a small error in your calculation. When converting the molar mass of oxygen from grams to kilograms, you should divide by Avogadro's number (6.022 x 10^23) instead of the number of oxygen molecules (6.5 x 10^19).

So the correct mass would be: m = (32/6.022e23) = 5.31e-25 kg

Plugging this into your equation, the rms speed would be: v = sq rt(3(1.38e-23)(445.93)/5.31e-25) = 472.3 m/s

This is a much higher speed than you initially calculated, which makes sense since the temperature is higher in this scenario.
 

1. What is the Kinetic Theory of Gases?

The Kinetic Theory of Gases is a scientific theory that explains the behavior of gases at a molecular level. It states that gases are made up of tiny particles in constant, random motion and that their kinetic energy is directly related to their temperature.

2. How do oxygen molecules move according to the Kinetic Theory?

Oxygen molecules, like all other gas molecules, move in a straight line until they collide with other molecules or the walls of their container. They move at different speeds depending on their temperature, with higher temperatures resulting in faster speeds.

3. What is the speed of oxygen molecules at room temperature?

At room temperature (around 25 degrees Celsius), the average speed of oxygen molecules is approximately 500 meters per second. However, individual molecules can have speeds ranging from 400 to 600 meters per second.

4. How does the speed of oxygen molecules change with temperature?

According to the Kinetic Theory, the speed of oxygen molecules is directly proportional to the temperature of the gas. As the temperature increases, the molecules gain more kinetic energy and move at higher speeds.

5. How does the Kinetic Theory explain the properties of gases, such as pressure and volume?

The Kinetic Theory explains that the pressure of a gas is caused by the constant collisions of gas molecules on the walls of their container. As the temperature and speed of the molecules increase, so does the pressure. This theory also explains why gases can be compressed or expand to fill their container, as the molecules are free to move and have no definite shape or volume.

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