If 1.204 x 10²¹ molecules of H₂SO₄ are removed from 392 mg of H₂SO₄, find the moles of H₂SO₄ left.

The correct option is 2 x 10^-3.

To find the moles of H₂SO₄ left, we need to calculate the initial moles of H₂SO₄, the moles of H₂SO₄ removed, and then subtract the removed moles from the initial moles.

Step 1: Calculate the molar mass of H₂SO₄
The chemical formula of sulfuric acid is H₂SO₄.
Atomic mass of Hydrogen (H) = 1 g/mol
Atomic mass of Sulfur (S) = 32 g/mol
Atomic mass of Oxygen (O) = 16 g/mol
Molar mass of H₂SO₄ = (2 x 1) + 32 + (4 x 16) = 2 + 32 + 64 = 98 g/mol.

Step 2: Calculate the initial moles of H₂SO₄
The initial mass of H₂SO₄ is 392 mg.
Converting milligrams (mg) to grams (g):
392 mg = 392 x 10^-3 g = 0.392 g.
Now, we calculate the initial moles using the formula:
$$\text{Initial moles}=\frac{\text{Given mass}}{\text{Molar mass}}$$
Substituting the values:
$$\text{Initial moles}=\frac{392\times {10}^{-3}\text{ g}}{98\text{ g/mol}}=4\times {10}^{-3}\text{ moles}$$
So, the initial moles of H₂SO₄ is 4 x 10^-3 moles.

Step 3: Calculate the moles of H₂SO₄ removed
The number of molecules removed is 1.204 x 10²¹ molecules.
Avogadro's number (N_A) = 6.022 x 10²³ molecules/mol.
We calculate the moles removed using the formula:
$$\text{Moles removed}=\frac{\text{Number of molecules}}{N_A}$$
Substituting the values:
$$\text{Moles removed}=\frac{1.204\times {10}^{21}}{6.022\times {10}^{23}}$$
Simplifying the division:
$$\text{Moles removed}=0.2\times {10}^{-2}=2\times {10}^{-3}\text{ moles}$$
So, the moles of H₂SO₄ removed is 2 x 10^-3 moles.

Step 4: Calculate the moles of H₂SO₄ left
Subtract the moles removed from the initial moles:
$$\text{Moles left}=\text{Initial moles}-\text{Moles removed}$$
Substituting the values:
$$\text{Moles left}=(4\times {10}^{-3})-(2\times {10}^{-3})$$
Factoring out 10^-3:
$$\text{Moles left}=(4-2)\times {10}^{-3}=2\times {10}^{-3}\text{ moles}$$
Therefore, the moles of H₂SO₄ left is 2 x 10^-3 moles.