Question

A mole of helium gas contains $6.02\text{ x 1}{{\text{0}}^{23}}$ helium atoms. How many helium atoms are there in a millimoles of helium? In a kilomole?

Answer 1

Hint: To find the value or number of helium atoms in millimoles, then we have to divide the value of millimoles by the number of helium atoms in one mole of helium gas, and to find the number of helium atoms in kilomole, then we have to multiply the value of kilomole to the number of helium atoms in one mole of helium gas.

Complete answer:
In the question, we are given that 1 mole of helium gas contains $6.02\text{ x 1}{{\text{0}}^{23}}$ of helium atoms and we have to find the number of atoms in millimoles and kilomoles.
We can relate the millimoles and the kilomole with millimeters and kilometers. We know that 1 meter is equal to 1000 millimeters, so we can say 1 mole will be equal to 1000 millimole.
To find the value or number of helium atoms in millimoles, then we have to divide the value of millimoles by the number of helium atoms in one mole of helium gas. We can write:
$1\text{ millimole = }\dfrac{6.02\text{ x 1}{{\text{0}}^{23}}}{1000}=6.02\text{ x 1}{{\text{0}}^{20}}$
Therefore, in 1 millimole of helium gas $6.02\text{ x 1}{{\text{0}}^{20}}$ helium atoms are present.
We know that 1 kilometer is equal to 1000 meters, so we can say that 1 kilomole is equal to 1000 moles.
To find the number of helium atoms in kilomole, then we have to multiply the value of kilomole to the number of helium atoms in one mole of helium gas. We can write:
$1\text{ kilomole = }6.02\text{ x 1}{{\text{0}}^{23}}\text{ x 1000}=6.02\text{ x 1}{{\text{0}}^{26}}$
Therefore, in 1 kilomole of helium gas $6.02\text{ x 1}{{\text{0}}^{26}}$ helium atoms are present.

Note:
Don't get confused about whether to multiply or divide the value, when we have to find the smaller value then we have to divide and when we have to find the larger value then we have to multiply.