Ethanol is the substance commonly called alcohol. The denisty of liquid alcohol is `0.8 gm//ml` at 293 K. if 1.2 mole of ethanol are needed for a particular experiment, what volume of ethanol should be measured out?

Options

A. 55.2 ml
B. 57.5 ml
C. 69ml
D. 47.9ml

Answer

To solve the problem of how much volume of ethanol is needed for 1.2 moles, we can follow these steps:

### Step 1: Identify the given data
- Moles of ethanol (n) = 1.2 moles
- Density of ethanol (d) = 0.8 g/ml
- Molecular weight of ethanol (M) = 46 g/mol

### Step 2: Use the formula for moles
The number of moles (n) can be expressed in terms of mass (m) and molecular weight (M) as follows:
\[ n = \frac{m}{M} \]
Where:
- \( m \) is the mass of the substance in grams
- \( M \) is the molecular weight in g/mol

### Step 3: Express mass in terms of volume and density
We know that mass can also be expressed in terms of volume (V) and density (d):
\[ m = d \times V \]
Where:
- \( V \) is the volume in ml
- \( d \) is the density in g/ml

### Step 4: Combine the equations
Substituting the expression for mass into the moles equation gives:
\[ n = \frac{d \times V}{M} \]

### Step 5: Rearranging the formula to find volume
We can rearrange the equation to solve for volume (V):
\[ V = \frac{n \times M}{d} \]

### Step 6: Plug in the values
Now we can substitute the known values into the equation:
- \( n = 1.2 \) moles
- \( M = 46 \) g/mol
- \( d = 0.8 \) g/ml

So,
\[ V = \frac{1.2 \, \text{moles} \times 46 \, \text{g/mol}}{0.8 \, \text{g/ml}} \]

### Step 7: Calculate the volume
Calculating the above expression:
\[ V = \frac{55.2 \, \text{g}}{0.8 \, \text{g/ml}} = 69 \, \text{ml} \]

### Conclusion
The volume of ethanol required for the experiment is **69 ml**.

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