What volume of a liquid (in L) will contain 10 mole ? If molar mass of liquid is 280 and its density is 1.4 g/mL.

Options

A. 2 L
B. 4 L
C. 7 L
D. 9 L

Answer

To find the volume of a liquid that contains 10 moles, given its molar mass and density, we can follow these steps:

### Step 1: Calculate the mass of the liquid
We know that the number of moles (n) is related to mass (m) and molar mass (M) by the formula:
\[ n = \frac{m}{M} \]
Rearranging this gives us:
\[ m = n \times M \]

Given:
- Number of moles, \( n = 10 \) moles
- Molar mass, \( M = 280 \) g/mol

Now, substituting the values:
\[ m = 10 \, \text{moles} \times 280 \, \text{g/mol} = 2800 \, \text{grams} \]

### Step 2: Use the density to find the volume
Density (d) is defined as:
\[ d = \frac{m}{V} \]
Where:
- \( d \) is the density,
- \( m \) is the mass,
- \( V \) is the volume.

Rearranging this gives us:
\[ V = \frac{m}{d} \]

Given:
- Mass, \( m = 2800 \, \text{grams} \)
- Density, \( d = 1.4 \, \text{g/mL} \)

Now, substituting the values:
\[ V = \frac{2800 \, \text{grams}}{1.4 \, \text{g/mL}} \]

### Step 3: Calculate the volume in mL
Performing the division:
\[ V = \frac{2800}{1.4} = 2000 \, \text{mL} \]

### Step 4: Convert mL to L
Since 1 L = 1000 mL, we convert the volume from mL to L:
\[ V = \frac{2000 \, \text{mL}}{1000} = 2 \, \text{L} \]

### Final Answer
The volume of the liquid that will contain 10 moles is **2 liters**.

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