`6.02 xx 10^(21)` molecules of urea are present in 1000ml of its solution. The concentration of urea solution is

Options

A. `0.001M`
B. `0.01M`
C. `0.02M`
D. `0.1M`

Answer

To find the concentration of urea solution in terms of molarity, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the number of molecules of urea**:
We are given that there are \(6.02 \times 10^{21}\) molecules of urea.

2. **Convert molecules to moles**:
We know that 1 mole of any substance contains \(6.02 \times 10^{23}\) molecules (Avogadro's number).
To find the number of moles of urea, we use the formula:
\[ \text{Number of moles} = \frac{\text{Number of molecules}}{6.02 \times 10^{23}} \]
Substituting the given number of molecules:
\[ \text{Number of moles} = \frac{6.02 \times 10^{21}}{6.02 \times 10^{23}} = \frac{6.02}{6.02} \times 10^{21 - 23} = 1 \times 10^{-2} \text{ moles} \]
Thus, the number of moles of urea is \(0.01\) moles.

3. **Convert the volume of the solution from mL to L**:
The volume of the solution is given as 1000 mL. To convert this to liters:
\[ 1000 \text{ mL} = 1 \text{ L} \]

4. **Calculate the molarity (concentration)**:
Molarity (M) is defined as the number of moles of solute per liter of solution:
\[ \text{Molarity} = \frac{\text{Number of moles}}{\text{Volume in L}} = \frac{0.01 \text{ moles}}{1 \text{ L}} = 0.01 \text{ M} \]

5. **Final answer**:
The concentration of the urea solution is \(0.01 \text{ M}\).