`500 mL` of a glucose solution contains `6.02 xx 10^(22)` molecules. The concentration of the solution is :

Options

A. `0.1 M`
B. `1.0M`
C. `0.2M`
D. `2.0M`

Explanation

To find the concentration of the glucose solution, we will follow these steps:

### Step 1: Convert the volume of the solution from mL to L
Given:
- Volume of the solution = 500 mL

To convert mL to L, we use the conversion factor:
\[ 1 \text{ L} = 1000 \text{ mL} \]
So,
\[ \text{Volume in L} = \frac{500 \text{ mL}}{1000} = 0.5 \text{ L} \]

### Step 2: Calculate the number of moles of glucose
We are given the number of molecules of glucose:
- Number of molecules = \( 6.02 \times 10^{22} \)

To find the number of moles, we use Avogadro's number:
\[ N_A = 6.022 \times 10^{23} \text{ molecules/mole} \]
The formula for calculating moles (\( n \)) is:
\[ n = \frac{\text{Number of molecules}}{N_A} \]
Substituting the values:
\[ n = \frac{6.02 \times 10^{22}}{6.022 \times 10^{23}} \]
Calculating this gives:
\[ n \approx 0.1 \text{ moles} \]

### Step 3: Calculate the molarity (concentration) of the solution
Molarity (\( M \)) is defined as the number of moles of solute per liter of solution:
\[ M = \frac{n}{\text{Volume in L}} \]
Substituting the values we have:
\[ M = \frac{0.1 \text{ moles}}{0.5 \text{ L}} \]
Calculating this gives:
\[ M = 0.2 \text{ M} \]

### Final Answer
The concentration of the glucose solution is \( 0.2 \text{ M} \).

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