An empty relative density bottle has a mass of 30g. When filled with paraffin, its mass is 70g. Calculate the mass of the bottle when it is filled with water. (relative density of papaffin =0.8)? 5 Answers Available Asked by Olayemi on 11th February, 2019

The mass of the empty bottle is $30 \text{ g}$.
The mass of the bottle filled with paraffin is $70 \text{ g}$.
The mass of the paraffin ($m_{\text{paraffin}}$) is the difference between these two masses:

$$m_{\text{paraffin}} = m_{\text{bottle+paraffin}} - m_{\text{empty}}$$ $$m_{\text{paraffin}} = 70 \text{ g} - 30 \text{ g}$$ $$m_{\text{paraffin}} = 40 \text{ g}$$

Relative density (RD) is defined as the ratio of the density of a substance to the density of water. For equal volumes, it is also the ratio of the mass of the substance to the mass of water.

$$\text{RD}_{\text{paraffin}} = \frac{m_{\text{paraffin}}}{m_{\text{water (same volume)}}}$$

We are given $\text{RD}_{\text{paraffin}} = 0.8$ and we found $m_{\text{paraffin}} = 40 \text{ g}$. We need to find $m_{\text{water (same volume)}}$.

$$0.8 = \frac{40 \text{ g}}{m_{\text{water (same volume)}}}$$

Rearrange the formula to solve for $m_{\text{water (same volume)}}$:

$$m_{\text{water (same volume)}} = \frac{40 \text{ g}}{0.8}$$ $$m_{\text{water (same volume)}} = 50 \text{ g}$$

The mass of the bottle filled with water ($m_{\text{bottle+water}}$) is the sum of the mass of the empty bottle and the mass of the water that fills it:

$$m_{\text{bottle+water}} = m_{\text{empty}} + m_{\text{water (same volume)}}$$ $$m_{\text{bottle+water}} = 30 \text{ g} + 50 \text{ g}$$ $$m_{\text{bottle+water}} = 80 \text{ g}$$

The final answer is $\text{80 g}$.