If 500mL of a 5M solution is diluted to 1500 mL, what will be the molarity of the solution obtained?

Options

A. 1.5 M
B. 1.66 M
C. 0.017 M
D. 1.59 M

Explanation

To solve the problem of finding the molarity of a solution after dilution, we can follow these steps:

### Step 1: Calculate the number of moles in the initial solution.
We start with a 5 M (molar) solution and a volume of 500 mL. To find the number of moles, we can use the formula:

\[ \text{Moles} = \text{Molarity} \times \text{Volume in Liters} \]

First, convert the volume from mL to L:

\[ 500 \, \text{mL} = \frac{500}{1000} = 0.5 \, \text{L} \]

Now, calculate the moles:

\[ \text{Moles} = 5 \, \text{M} \times 0.5 \, \text{L} = 2.5 \, \text{moles} \]

### Step 2: Understand that the number of moles remains constant during dilution.
When we dilute a solution, the number of moles of solute does not change. Therefore, we still have 2.5 moles of solute after dilution.

### Step 3: Calculate the new volume after dilution.
The new volume after dilution is given as 1500 mL. Convert this to liters:

\[ 1500 \, \text{mL} = \frac{1500}{1000} = 1.5 \, \text{L} \]

### Step 4: Calculate the new molarity of the solution.
Now, we can find the new molarity (M) using the formula:

\[ \text{Molarity} = \frac{\text{Moles}}{\text{Volume in Liters}} \]

Substituting the values we have:

\[ \text{Molarity} = \frac{2.5 \, \text{moles}}{1.5 \, \text{L}} = \frac{2.5}{1.5} \approx 1.67 \, \text{M} \]

### Final Answer:
The molarity of the solution obtained after dilution is approximately **1.67 M**.

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