Q.How much positive and negative charge is there in a cup of water? (Assume the mass of one cup of water to be $250\,\text{g}$.)

Water is electrically neutral, but each molecule packs equal amounts of positive (protons) and negative (electrons) charge. We count one kind; the other is equal in magnitude.

1. Moles of water. Molar mass of $\text{H}_2\text{O}=18\,\text{g/mol}$, so $250\,\text{g}$ is

2. Molecules. $N=nN_A=13.9\times6.022\times10^{23}=8.36\times10^{24}.$
3. Protons (or electrons) per molecule. $\text{H}_2\text{O}$ has $2(1)+8=10$ of each.
4. Total positive charge. …

This question is about the charge that matter contains, not any net charge it carries. Every neutral molecule holds equal positive and negative charge; the task is to work out how large each of those is for a cup of water.

Step 1 — Number of moles.

The molar mass of water is $M=2(1)+16=18\,\text{g/mol}$, so

Step 2 — Number of molecules.

Step 3 — Charges per molecule.

Each $\text{H}_2\text{O}$ has $2$ hydrogen atoms ($1$ proton each) and $1$ oxygen atom ($8$ protons), i.e. $10$ protons and, being neutral, $10$ electrons.

Step 4 — Total positive charge.

Total protons $=10N=8.36\times10^{25}$, so …

Method: Atomic Charge Counting via Avogadro's Number

This method uses the fact that every atom in water is electrically neutral overall, but contains equal amounts of positive charge (in protons) and negative charge (in electrons). We count the total number of each type of charge carrier.

Step 1: Find the number of water molecules

• Molar mass of water ($\text{H}_2\text{O}$): $2 \times 1 + 16 = 18\ \text{g/mol}$
• Number of moles in $250\ \text{g}$ of water: $\displaystyle n = \frac{250}{18} \approx 13.89\ \text{mol}$
• Using Avogadro's number ($N_A = 6.022 \times 10^{23}\ \text{mol}^{-1}$): $\displaystyle N_{\text{molecules}} = n \times N_A \approx 13.89 \times 6.022 \times 10^{23} \approx 8.36 \times 10^{24}\ \text{molecules}$

Step 2: Count protons and electrons per molecule

Each water molecule has:

• 10 electrons (8 from oxygen + 1 from each hydrogen)
• 10 protons (8 from oxygen + 1 from each hydrogen)

So total number of protons = total number of electrons:

$\displaystyle N_{\text{protons}} = N_{\text{electrons}} = 10 \times 8.36 \times 10^{24} = 8.36 \times 10^{25}$

Step 3: Compute the total charge

Charge of one proton: $+e = +1.602 \times 10^{-19}\ \text{C}$ …

Common Mistakes: Charge in a Cup of Water

Students often make predictable errors on this question. Here are the most common ones — and how to avoid each.

1. Forgetting that water is electrically neutral

Mistake:

Students calculate only the number of electrons or protons, then report that as the net charge.

Why it’s wrong:

A cup of water has equal numbers of protons and electrons. The net charge is zero. The question asks for the amount of positive and negative charge separately, not the net charge.

How to avoid:

Always start by stating: “Water is neutral — total positive charge equals total negative charge.” Then calculate the magnitude of one type.

2. Using the wrong molecular formula or atomic numbers

Mistake:

Treating water as $\text{H}_2\text{O}$ but forgetting that:

• Hydrogen has 1 proton (atomic number $Z=1$)
• Oxygen has 8 protons ($Z=8$)

So total protons per water molecule = $1+1+8 = 10$.

How to avoid:

Write it down explicitly:

3. Confusing mass with number of molecules

Mistake:

Using $250\,\text{g}$ directly without converting to moles.

How to avoid:

Always use the molar mass:

• Molar mass of water = $18\,\text{g/mol}$
• Number of moles = $\frac{250}{18} \approx 13.89\,\text{mol}$
• Number of molecules = $13.89 \times 6.022 \times 10^{23}$

4. Using the wrong value for elementary charge

Mistake:

Using $e = 1.6 \times 10^{-19}\,\text{C}$ but forgetting that proton charge is $+e$ and electron charge is $-e$.

How to avoid:

Write clearly:

• Charge of one proton = $+1.6 \times 10^{-19}\,\text{C}$
• Charge of one electron = $-1.6 \times 10^{-19}\,\text{C}$

5. Reporting the answer with wrong sign or units …