Question

# Collision diameter is least in case of:

Hint: Recall the collision theory of chemical reactions under the chemical kinetics chapter. The collision diameter is inversely proportional to the molar mass of the molecule. This is because as the molar mass increases, size of the atom increases as well reducing electron repulsions.
${{d}_{{}}}\alpha \dfrac{1}{M}$
Where,
d is the collision diameter,
M is the molecular mass of the molecule.

-Collision theory states that for a chemical reaction to occur, the reacting particles must collide with one another.
-The rate of the reaction depends on the frequency of collisions. The three main points of collision theory for a chemical reaction to take place are:
- Reacting substances must collide
- The colliding particles should have sufficient energy
- The substances must collide in a set orientation.
-Collision diameter is defined as the distance between the centers of two colliding molecules when at their closest point of approach.
-Collision diameter is inversely proportional to the molecular mass of the molecule. This is because the molecules with higher molecular mass have a greater radius.
${{d}_{{}}}\alpha \dfrac{1}{M}$
-Since the size of the atom is big, there is a lot of free space and the electron density is relatively less. Due to this the atoms can come close due to reduced electron-electron repulsions.
Let us calculate the molecular mass of the molecules mentioned in the options:
${{H}_{2}}$ has a molecular mass of 2 g
$He$ has a molecular mass of 4 g
$C{{O}_{2}}$ has a molecular mass of 44 g
${{N}_{2}}$ has a molecular mass of 28 g
$C{{O}_{2}}$ has the highest molecular mass and will have the least collision diameter.

Therefore, the correct answer is option (C).

Note:
It is important to remember that an increase in molecular mass also results in the increase of electrons. However, the electrons are far apart due to the large size of the atom and hence the electron repulsions decrease.