# Rate of collisions of molecules in a container

• Linus Pauling
In summary, the rms speed of nitrogen molecules at 100C in a container with a 10cm x 10cm square wall and a pressure of 2.0 atm is 576 m/s. To calculate the collision rate, the equation N_coll / deltaT = 0.5(n/V)*Avogadro's*v_x can be used, where n/V is obtained from the ideal gas law and multiplied by Avogadro's number. The resulting units for collision rate are m^-1 s^-1.
Linus Pauling
1. At 100C the rms speed of nitrogen molecules is 576 m/s. Nitrogen at 100C and a pressure of 2.0 atm is held in a container with a 10cm x 10cm square wall.

2. N_coll / deltaT = 0.5(N/V)*A*v_x

3. I know that I have to use v_rms/3 = v_x = 192 m/s, and the area will be 0.01 m^2. Is (N/V) simply n/V from the ideal gas law? If so, I calculate it to be:

n/V = 65.35 mol/m^2, and would I multiply by Avogadro's to obtain 3.94*10^-21 m^-2?

But then the units of (N/V) and A would cancel, leaving with units of m/s because of v_x, and I need units in inverse seconds.

?

N_coll / deltaT = 0.5(n/V)*Avogadro's*v_x N_coll / deltaT = 0.5*3.94*10^-21 m^-2 * 192 m/s N_coll / deltaT = 3.48*10^-23 m^-1 s^-1

I would first clarify the parameters and assumptions of the experiment. Is the container a perfect vacuum or is there some gas present? Is the container at a constant temperature and pressure? These factors can significantly affect the rate of collisions of molecules in the container.

Assuming that the container is filled with nitrogen gas at a constant temperature and pressure, we can use the ideal gas law to determine the number of moles of gas present (n/V). This value can then be multiplied by Avogadro's number to obtain the number of molecules per unit volume (N/V).

Using the given value of the rms speed of nitrogen molecules at 100C, we can calculate the average speed of molecules in the x-direction (v_x) using the formula v_rms/3 = v_x. This value can then be multiplied by the area of the container wall (A) to obtain the total number of collisions per unit time (N_coll/deltaT).

However, it is important to note that this calculation assumes a perfectly elastic collision between molecules and the container wall. In reality, there will be some loss of energy due to intermolecular forces and the size of the molecules. Therefore, the actual rate of collisions may be lower than the calculated value.

Additionally, it is important to consider the size and shape of the container. A 10cm x 10cm square wall may not accurately represent the entire container, as there may be unaccounted for walls and spaces within the container. This could affect the overall rate of collisions.

In conclusion, the rate of collisions of molecules in a container is a complex phenomenon that is affected by various factors and assumptions. Using the given information, we can estimate the rate of collisions, but it is important to acknowledge the limitations and potential errors in the calculation. Further experimentation and analysis may be necessary to obtain a more accurate and comprehensive understanding of this phenomenon.

## 1. What is the meaning of the rate of collisions of molecules in a container?

The rate of collisions of molecules in a container refers to the frequency at which molecules collide with each other within a specific volume of space. This is an important concept in chemistry and physics, as it helps to determine the rate of chemical reactions and the behavior of gases.

## 2. How is the rate of collisions of molecules in a container measured?

The rate of collisions of molecules in a container can be measured using various experimental techniques, such as gas pressure measurements, spectroscopy, and molecular beam scattering. These methods allow scientists to observe the collisions between molecules and calculate the frequency of collisions.

## 3. What factors affect the rate of collisions of molecules in a container?

Several factors can affect the rate of collisions of molecules in a container, including temperature, pressure, and the number and type of molecules present in the container. Additionally, the size and shape of the container can also impact the rate of collisions.

## 4. How does the rate of collisions of molecules in a container relate to the kinetic theory of gases?

The kinetic theory of gases states that the pressure exerted by a gas is a result of the collisions between its molecules and the walls of the container. Therefore, the rate of collisions of molecules in a container is directly related to the pressure of the gas, as well as other properties such as temperature and volume.

## 5. Why is the rate of collisions of molecules in a container important in chemical reactions?

The rate of collisions of molecules in a container is crucial in chemical reactions because it determines how often reactant molecules will come into contact with each other and potentially form new products. The higher the rate of collisions, the faster the reaction will occur, and vice versa.

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