An aqueous solution contains `980` mg of `H_(2)SO_(4)`, `3.01xx10^(21)` molecules of `H_(2)SO_(4)` are removed from this solution. How many moles of `H_(2)SO_(4)` are left in the resultant solution.

Options

A. `5` mole
B. `0.005` mole
C. `0.05` mole
D. `50` mole

Explanation

To solve the problem step by step, we need to determine how many moles of \( H_2SO_4 \) are left in the solution after removing a certain number of molecules.

### Step 1: Calculate the initial number of moles of \( H_2SO_4 \)

We start with the mass of \( H_2SO_4 \) given in the problem:

\[ \text{Mass of } H_2SO_4 = 980 \text{ mg} = 980 \times 10^{-3} \text{ g} = 0.980 \text{ g} \]

Next, we need to find the molar mass of \( H_2SO_4 \):

\[ \text{Molar mass of } H_2SO_4 = 98 \text{ g/mol} \]

Now, we can calculate the number of moles using the formula:

\[ \text{Number of moles} (n) = \frac{\text{Given mass}}{\text{Molar mass}} = \frac{0.980 \text{ g}}{98 \text{ g/mol}} = 0.01 \text{ mol} \]

### Step 2: Calculate the number of molecules in the initial solution

Using Avogadro's number, which is \( 6.022 \times 10^{23} \) molecules/mol, we can find the total number of molecules in the initial amount of \( H_2SO_4 \):

\[ \text{Number of molecules} = n \times \text{Avogadro's number} = 0.01 \text{ mol} \times 6.022 \times 10^{23} \text{ molecules/mol} = 6.022 \times 10^{21} \text{ molecules} \]

### Step 3: Calculate the number of molecules left after removal

We are given that \( 3.01 \times 10^{21} \) molecules of \( H_2SO_4 \) are removed from the solution. Therefore, the number of molecules left in the solution is:

\[ \text{Molecules left} = \text{Initial molecules} - \text{Removed molecules} = 6.022 \times 10^{21} - 3.01 \times 10^{21} = 3.012 \times 10^{21} \text{ molecules} \]

### Step 4: Calculate the number of moles of \( H_2SO_4 \) remaining

To find the number of moles corresponding to the remaining molecules, we use the formula:

\[ \text{Number of moles left} = \frac{\text{Molecules left}}{\text{Avogadro's number}} = \frac{3.012 \times 10^{21} \text{ molecules}}{6.022 \times 10^{23} \text{ molecules/mol}} \]

Calculating this gives:

\[ \text{Number of moles left} = 0.005 \text{ mol} \]

### Final Answer

Thus, the number of moles of \( H_2SO_4 \) left in the resultant solution is:

\[ \boxed{0.005 \text{ mol}} \]