Given the density of the chloroform is `1.510gcm^-3` , then the volume occupied by 20.050 g of chloroform (upto correct significant figures) is

Options

A. `13.3cm^3`
B. `13.278cm^3`
C. `13.28cm^3`
D. `13.2780cm^3`

Answer

To find the volume occupied by 20.050 g of chloroform given its density, we can use the formula for density:

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

We can rearrange this formula to find the volume:

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

### Step-by-Step Solution:

1. **Identify the given values**:
- Density of chloroform = \(1.510 \, \text{g/cm}^3\)
- Mass of chloroform = \(20.050 \, \text{g}\)

2. **Substitute the values into the volume formula**:
\[ \text{Volume} = \frac{20.050 \, \text{g}}{1.510 \, \text{g/cm}^3} \]

3. **Perform the calculation**:
\[ \text{Volume} = \frac{20.050}{1.510} \approx 13.2874 \, \text{cm}^3 \]

4. **Round to the correct number of significant figures**:
- The mass (20.050 g) has 5 significant figures.
- The density (1.510 g/cm³) has 4 significant figures.
- Therefore, the final answer should be rounded to 4 significant figures (the least number of significant figures from the given values).
- Rounding \(13.2874 \, \text{cm}^3\) to 4 significant figures gives us \(13.29 \, \text{cm}^3\).

5. **Final Answer**:
\[ \text{The volume occupied by 20.050 g of chloroform is } 13.29 \, \text{cm}^3. \]