What is the molarity of an aqueous solution of ethyl alcohol molar mass =46.0 which contains 50.0 g of alcohol in 500 mL of the solution?

Explanation

To find the molarity of the aqueous solution of ethyl alcohol, we can follow these steps:

### Step 1: Identify the given data
- Molar mass of ethyl alcohol = 46.0 g/mol
- Mass of ethyl alcohol = 50.0 g
- Volume of the solution = 500 mL

### Step 2: Convert the volume from mL to L
Since molarity is expressed in moles per liter, we need to convert the volume from milliliters to liters:
\[ \text{Volume in liters} = \frac{500 \text{ mL}}{1000} = 0.5 \text{ L} \]

### Step 3: Calculate the number of moles of ethyl alcohol
To find the number of moles, we use the formula:
\[ \text{Number of moles} = \frac{\text{mass}}{\text{molar mass}} \]
Substituting the values:
\[ \text{Number of moles} = \frac{50.0 \text{ g}}{46.0 \text{ g/mol}} \approx 1.08696 \text{ moles} \]

### Step 4: Calculate the molarity of the solution
Molarity (M) is defined as the number of moles of solute per liter of solution:
\[ \text{Molarity} = \frac{\text{Number of moles}}{\text{Volume in L}} \]
Substituting the values:
\[ \text{Molarity} = \frac{1.08696 \text{ moles}}{0.5 \text{ L}} \approx 2.17392 \text{ M} \]

### Step 5: Round the answer
We can round the molarity to three significant figures:
\[ \text{Molarity} \approx 2.17 \text{ M} \]

### Final Answer:
The molarity of the aqueous solution of ethyl alcohol is approximately **2.17 M**.

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