Two atoms with charges of +1 and -1 are separated by a distance of 0.5 angstroms. What would happen to the lattice energy between ions if the distance increases to 2 angstroms?
A. The lattice energy decreases by a factor of 4.
B. The lattice energy increases by a factor of 16.
C. The lattice energy decreases by a factor of 16.
D. The lattice energy increases by a factor of 4.
the answer was c in case you were wondering
If anyone wanted to know how to solve it for next time you need the equation for the force of attraction. It is (F1 * F2)/(r^2)
In this problem F1 is +1 F2 is -1 and r= 0.5 and then 2.
Plug the values in,(r= 0.5) you should get F= -4
Plug the values in the second time, this time with r= 2
You should get -0.25
Compare the 2 answers and you should see that the lattice energy decreases by a factor of 16.
I always have trouble with these because one never knows how negative numbers are counted when they increase or decrease. In addition the definition of lattice energy depends upon which book is used. Here is my reasoning. But first, the change is from 0.5 to 2 which is squared distance or 0.25 to 4 which is a factor of 16. So the answer must be B or C.
If I have a MCl molecule(crystal), it takes energy to break up the crystal lattice. Let's call that value 1000 J and we must ADD it to break the crystal lattice. The lattice energy, U, is - crystal energy so U = -1000 J. Now, if we separate MCl by a factor or 4, it will be easier to break the crystal; let's say that is +500. Now U = -500. If U changed from -1000 to -500 that is a less negative number so i say it increases. I would choose B.
Between CsCl and BaCl2 compare lattice energy
To determine what would happen to the lattice energy between ions when the distance between them increases, we need to understand Coulomb's law.
Coulomb's law states that the force between two charged particles is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
Mathematically, it can be expressed as:
F = k * (q1 * q2) / r^2
Where:
F is the force between the two charges,
k is the electrostatic constant,
q1 and q2 are the charges of the particles, and
r is the distance between them.
In this case, we have two ions with charges of +1 and -1. Let's assume that the lattice energy is directly related to the force between them.
If we compare the force between the ions at the initial distance of 0.5 angstroms to the force at the new distance of 2 angstroms, we can see that the distance has increased by a factor of 4 (2 angstroms / 0.5 angstroms = 4).
According to Coulomb's law, the force is inversely proportional to the square of the distance. So, when the distance increases by a factor of 4, the force will decrease by a factor of 4^2 = 16.
Since the lattice energy is directly related to the force between the ions, when the distance increases to 2 angstroms, the lattice energy decreases by a factor of 16.
Therefore, the correct answer is:
C. The lattice energy decreases by a factor of 16.