A relative density bottle has a mass of 19 g wh... - JAMB Physics 2023 Question

The relative density (also known as specific gravity) of a substance is the ratio of its density to the density of water. In this case, the relative density of alcohol (\(RD_{\text{alcohol}}\)) is given as 0.8.

The formula for relative density is:

\[ RD = \frac{\text{Density of substance}}{\text{Density of water}} \]

Given that the mass of the empty bottle is 19 g and when filled with water is 66 g, we can find the volume of water using the formula:

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

Now, let's find the volume of water (\(V_{\text{water}}\)):

\[ V_{\text{water}} = \frac{\text{Mass of water}}{\text{Density of water}} = \frac{66 \, \text{g}}{1 \, \text{g/cm}^3} \]

Since the density of water is approximately \(1 \, \text{g/cm}^3\).

Now, we can find the volume of alcohol (\(V_{\text{alcohol}}\)) that would have the same mass as the water, given that \(RD_{\text{alcohol}} = 0.8\):

\[ V_{\text{alcohol}} = \frac{V_{\text{water}}}{RD_{\text{alcohol}}} = \frac{66 \, \text{g}}{0.8} \]

Finally, calculate the mass of the bottle when filled with alcohol:

\[ \text{Mass}_{\text{alcohol}} = \text{Mass}_{\text{empty}} + \text{Mass}_{\text{water}} \]

\[ \text{Mass}_{\text{alcohol}} = 19 \, \text{g} + \text{Mass}_{\text{alcohol}} \]

Now, solve for the mass of the bottle when filled with alcohol.

Let's perform the calculations:

\[ V_{\text{water}} = \frac{66}{1} = 66 \, \text{cm}^3 \]

\[ V_{\text{alcohol}} = \frac{66}{0.8} = 82.5 \, \text{cm}^3 \]

\[ \text{Mass}_{\text{alcohol}} = 19 + \frac{66}{0.8} = 19 + 82.5 = 101.5 \, \text{g} \]

Therefore, the correct option is: 56.6 g