The molarity of a solution containing 50g of NaCl in 500g of a solution and having a density of `0.936 "g/cm"^(3)` is :

Options

A. 1.5 M
B. 1.6 M
C. 1.8 M
D. 1.2 M

Explanation

To find the molarity of the solution containing 50 g of NaCl in 500 g of solution with a density of 0.936 g/cm³, we can follow these steps:

### Step 1: Calculate the volume of the solution
Given the density of the solution (0.936 g/cm³), we can find the volume of 500 g of solution using the formula:

\[ \text{Volume} = \frac{\text{Mass}}{\text{Density}} \]

Substituting the values:

\[ \text{Volume} = \frac{500 \, \text{g}}{0.936 \, \text{g/cm}^3} \]

Calculating this gives:

\[ \text{Volume} = 534.3 \, \text{cm}^3 \]

### Step 2: Convert volume from cm³ to liters
Since molarity is expressed in moles per liter, we need to convert the volume from cm³ to liters:

\[ \text{Volume in liters} = \frac{534.3 \, \text{cm}^3}{1000} = 0.5343 \, \text{L} \]

### Step 3: Calculate the number of moles of NaCl
Next, we need to find the number of moles of NaCl. The molar mass of NaCl is approximately 58.5 g/mol. We can calculate the number of moles using the formula:

\[ \text{Number of moles} = \frac{\text{Mass}}{\text{Molar mass}} \]

Substituting the values:

\[ \text{Number of moles} = \frac{50 \, \text{g}}{58.5 \, \text{g/mol}} \]

Calculating this gives:

\[ \text{Number of moles} \approx 0.8547 \, \text{mol} \]

### Step 4: Calculate the molarity of the solution
Now we can calculate the molarity using the formula:

\[ \text{Molarity} = \frac{\text{Number of moles}}{\text{Volume in liters}} \]

Substituting the values:

\[ \text{Molarity} = \frac{0.8547 \, \text{mol}}{0.5343 \, \text{L}} \]

Calculating this gives:

\[ \text{Molarity} \approx 1.60 \, \text{M} \]

### Final Answer
The molarity of the solution is approximately **1.60 M**.

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