An empty density bottle weighs 30 g, and 54 g when filled with kerosene. If the volume of the bottle is 30 ml, find the density of kerosene in (a) `"g/cm"^3` (b)`"kg/m"^3` .Also find its RD.

Answer

To solve the problem step by step, we will follow the given data and apply the relevant formulas for density and relative density.

### Step 1: Identify the given data
- Mass of the empty density bottle (m_empty) = 30 g
- Mass of the bottle when filled with kerosene (m_filled) = 54 g
- Volume of the bottle (V) = 30 ml

### Step 2: Calculate the mass of kerosene
To find the mass of the kerosene, we subtract the mass of the empty bottle from the mass of the filled bottle:
\[ m_{kerosene} = m_{filled} - m_{empty} = 54 \, \text{g} - 30 \, \text{g} = 24 \, \text{g} \]

### Step 3: Convert volume from ml to cm³
Since 1 ml is equivalent to 1 cm³, the volume of the bottle in cm³ is:
\[ V = 30 \, \text{ml} = 30 \, \text{cm}^3 \]

### Step 4: Calculate the density of kerosene
The formula for density (ρ) is given by:
\[ \rho = \frac{mass}{volume} \]
Substituting the values we have:
\[ \rho_{kerosene} = \frac{m_{kerosene}}{V} = \frac{24 \, \text{g}}{30 \, \text{cm}^3} = 0.8 \, \text{g/cm}^3 \]

### Step 5: Convert density to kg/m³
To convert the density from g/cm³ to kg/m³, we use the conversion factor (1 g/cm³ = 1000 kg/m³):
\[ \rho_{kerosene} = 0.8 \, \text{g/cm}^3 \times 1000 \, \text{kg/m}^3 = 800 \, \text{kg/m}^3 \]

### Step 6: Calculate the relative density (RD)
Relative density (RD) is defined as the ratio of the density of the substance to the density of water. The density of water is approximately 1 g/cm³.
\[ RD = \frac{\rho_{kerosene}}{\rho_{water}} = \frac{0.8 \, \text{g/cm}^3}{1 \, \text{g/cm}^3} = 0.8 \]

### Summary of Results
- Density of kerosene in g/cm³: **0.8 g/cm³**
- Density of kerosene in kg/m³: **800 kg/m³**
- Relative Density (RD): **0.8**