Question

The total charge in coulombs, of all the electrons in a three-gram mole hydrogen atom, is equal to $- x \times {10^3}C$ . Find the value of $x$ .
Use Avogadro number, ${N_A} = 6 \times {10^{23}}$ and charge on an electron $e = - 1.6 \times {10^{ - 19}}C$ .

Answer 1

3 gram-mole of hydrogen atoms means 3 moles of hydrogen atoms. The number of hydrogen atoms $=$ Number of moles of hydrogen atom $\times$ Avogadro’s constant. The total number of electrons in hydrogen atoms $=$ Number of hydrogen atoms $\times 1$ . Now finally calculate the total charge of all the electrons in three-gram mole hydrogen $=$ Total number of electrons $\times 1.6 \times {10^{ - 19}}$ .

Complete answer:
To solve this problem we have to first look at what gram-mole means
So 1 gram-mole in the simplest way is the weight of a substance in grams that is equal to the molar mass of that substance. Let’s take an example, consider we are given 3-gram moles of ${O_2}$ molecule. 1 gram-mole of ${O_2}$ molecules will weigh 16 grams (Molar mass of ${O_2}$ is 16amu). So, 3-gram moles of ${O_2}$ molecules will weigh 48 grams. Now, the important thing for us to note is the number of moles of ${O_2}$ molecules in 3 gram-moles of ${O_2}$ molecules.
So, $n = \dfrac{{Mass}}{{Molar{\text{ }}Mass}}$
$n =$ Moles of ${O_2}$ molecules
$Mass =$ Weight of ${O_2}$ molecules in grams
$Molar{\text{ }}Mass =$ The molar mass of ${O_2}$ molecules
So for ${O_2}$ molecules
$n = \dfrac{{48}}{{16}} = 3$ moles.
This means 1 mole-gram of a substance contains one mole of that substance.
Now, coming back to hydrogen atoms, we are given 3 mole-grams which means 3 moles of the hydrogen atom.
The number of hydrogen atoms $=$ moles $\times$ Avogadro’s constant
Number of hydrogen atoms $= 3 \times 6 \times {10^{23}}$
Number of hydrogen atoms $= 18 \times {10^{23}}$ atoms
Now, we also know that 1 hydrogen atom is the simplest and consists of 1 electron, 1 proton, and no neutrons.
So, the number of total electrons in $18 \times {10^{23}}$ hydrogen atoms will be
Total number of electrons $= 18 \times {10^{23}} \times 1$
Total number of electrons $= 18 \times {10^{23}}$ electrons
Now, we know that charge of 1 electron is $- 1.6 \times {10^{ - 19}}C$
So, the total charge in electrons of 3 gram-mole hydrogen $= 18 \times {10^{23}} \times 1.6 \times {10^{ - 19}} = - 2.88 \times {10^5}C$
We are given the question that the charge on electrons in 3 gram-mole hydrogen is $- x \times {10^3}C$ .
So, $- x \times {10^3} = - 2.88 \times {10^5}$
$x = 288$

Note:
In the solution, we discussed what gram-mole means by using the example of ${O_2}$ molecule, but you can skip this step and just mention that 1 gram-mole of a substance contains 3 moles of a substance and the weight of 1 mole-gram of a substance will be equal to the molar mass of the substance in grams.