A sample of `NaNO_(3)` weighing `0.38 g` is placed in a `50.0 mL` volumetric flask. The flask is then filled with water to the mark on the neck. What is the molarity of the solution?

Options

A. `8.94 xx 10^(-6)M`
B. `8.94 xx 10^(-2)M`
C. `1.94 xx 10^(-2)M`
D. `8.94 xx 10^(-4)M`

Answer

To find the molarity of the NaNO₃ solution, we will follow these steps:

### Step 1: Calculate the number of moles of NaNO₃
The number of moles (n) can be calculated using the formula:
\[ n = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]

Given:
- Mass of NaNO₃ = 0.38 g
- Molar mass of NaNO₃ = 85 g/mol (calculated as Na: 23 + N: 14 + O: 16*3)

Now, substituting the values:
\[ n = \frac{0.38 \, \text{g}}{85 \, \text{g/mol}} \]

### Step 2: Calculate the molarity (M)
Molarity (M) is defined as the number of moles of solute per liter of solution. The formula for molarity is:
\[ M = \frac{n}{V} \]
where \( V \) is the volume of the solution in liters.

Since the volume of the solution is given as 50.0 mL, we need to convert this to liters:
\[ V = 50.0 \, \text{mL} = 0.050 \, \text{L} \]

Now, substituting the values into the molarity formula:
\[ M = \frac{n}{0.050 \, \text{L}} \]

### Step 3: Substitute the number of moles into the molarity equation
Now we can substitute the value of \( n \) calculated in Step 1 into the molarity equation:
\[ M = \frac{0.38 \, \text{g}/85 \, \text{g/mol}}{0.050 \, \text{L}} \]

### Step 4: Calculate the final molarity
Now, perform the calculations:
1. Calculate the number of moles:
\[ n = \frac{0.38}{85} \approx 0.00447 \, \text{mol} \]
2. Calculate the molarity:
\[ M = \frac{0.00447 \, \text{mol}}{0.050 \, \text{L}} \approx 0.0894 \, \text{mol/L} \]

Thus, the molarity of the NaNO₃ solution is approximately:
\[ M \approx 0.0894 \, \text{M} \]

### Final Answer
The molarity of the solution is approximately **0.0894 M**.

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