What is the total charge, in coulombs, of all the electrons in three gram mole of hydrogen atom?

Explanation

To find the total charge of all the electrons in three gram moles of hydrogen atoms, we can follow these steps:

### Step 1: Determine the number of moles of hydrogen atoms
We are given that we have 3 grams of hydrogen. The molar mass of hydrogen (H) is approximately 1 gram/mole. Therefore, the number of moles of hydrogen can be calculated as follows:

\[ \text{Number of moles} = \frac{\text{mass}}{\text{molar mass}} = \frac{3 \text{ g}}{1 \text{ g/mole}} = 3 \text{ moles} \]

### Step 2: Calculate the number of hydrogen atoms
Using Avogadro's number, which is approximately \(6.022 \times 10^{23}\) atoms/mole, we can find the total number of hydrogen atoms in 3 moles:

\[ \text{Number of atoms} = \text{Number of moles} \times \text{Avogadro's number} = 3 \text{ moles} \times 6.022 \times 10^{23} \text{ atoms/mole} \]

Calculating this gives:

\[ \text{Number of atoms} = 3 \times 6.022 \times 10^{23} \approx 1.8066 \times 10^{24} \text{ atoms} \]

### Step 3: Determine the total number of electrons
Since each hydrogen atom has one electron, the total number of electrons is the same as the total number of hydrogen atoms:

\[ \text{Number of electrons} = 1.8066 \times 10^{24} \]

### Step 4: Calculate the total charge of the electrons
The charge of a single electron is approximately \(-1.6 \times 10^{-19}\) coulombs. Therefore, the total charge \(Q\) of all the electrons can be calculated by multiplying the number of electrons by the charge of one electron:

\[ Q = \text{Number of electrons} \times \text{Charge of one electron} \]
\[ Q = 1.8066 \times 10^{24} \times (-1.6 \times 10^{-19}) \]

Calculating this gives:

\[ Q \approx -2.89056 \times 10^{5} \text{ coulombs} \]

### Final Answer
The total charge of all the electrons in three gram moles of hydrogen atoms is approximately \(-2.89 \times 10^{5}\) coulombs.