If `3*01xx10^(20)` molecules are removed from 98 mg of `H_(2)SO_(4)`, then the number of moles of `H_(2)SO_(4)` left are

Options

A. `0*1xx10^(-3)`
B. `0*5xx10^(-3)`
C. `1*66xx10^(-3)`
D. `9*95xx10^(-2)`

Explanation

To solve the problem step by step, we will follow these instructions:

### Step 1: Calculate the number of moles of H₂SO₄ removed
We know that the number of molecules removed is given as \(3.01 \times 10^{20}\) molecules. To find the number of moles removed, we use Avogadro's number (\(6.02 \times 10^{23}\) molecules/mole).

\[ \text{Number of moles removed} = \frac{\text{Number of molecules removed}}{\text{Avogadro's number}} = \frac{3.01 \times 10^{20}}{6.02 \times 10^{23}} \]

Calculating this gives:

\[ \text{Number of moles removed} = 0.5 \times 10^{-3} \text{ moles} \]

### Step 2: Calculate the initial number of moles of H₂SO₄
We are given that the mass of H₂SO₄ is 98 mg. First, we convert this mass into grams:

\[ 98 \text{ mg} = 98 \times 10^{-3} \text{ g} = 0.098 \text{ g} \]

Next, we need the molar mass of H₂SO₄, which is approximately 98 g/mol. We can now calculate the number of moles of H₂SO₄ initially present:

\[ \text{Number of moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} = \frac{0.098 \text{ g}}{98 \text{ g/mol}} = 1 \times 10^{-3} \text{ moles} \]

### Step 3: Calculate the number of moles of H₂SO₄ left
Now, we subtract the number of moles removed from the initial number of moles:

\[ \text{Number of moles left} = \text{Initial moles} - \text{Moles removed} = 1 \times 10^{-3} - 0.5 \times 10^{-3} \]

Calculating this gives:

\[ \text{Number of moles left} = 0.5 \times 10^{-3} \text{ moles} \]

### Final Answer
The number of moles of H₂SO₄ left is \(0.5 \times 10^{-3}\) moles.

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