Question

The mass of an empty density bottle is $30g$, it is $75g$ when filled completely with water and $65g$ when filled completely with a liquid. Find: a) volume of density bottle b) density of liquid and c) relative density of liquid

Answer 1

Step 1: Given data

The mass of the density bottle: $30g$

The mass of the bottle completely filled with water: $75g$

The mass of the bottle completely filled with liquid: $65g$

Step 2: Finding the volume of the bottle

We already know that the density of water is $1gm/cc$. Let the mass of the water filled in the bottle be $m$.

⇒ $75=30+m$

⇒ $m=45g$

Formula: $Density=\frac{mass}{volume}$

The volume of the density bottle $=\frac{mass}{density}$

⇒ volume of the density bottle is $\frac{45gm}{1gm/cc}$

The volume of the density bottle is $45cc$.

Step 3: Finding the density of the liquid

Let the density of the liquid be $d$. The volume occupied by water and liquid is the same.

Let the mass of the liquid be $m_2$

⇒ $65=30+m_2$

⇒ $m_2=35gm$

Now we know the masses of both liquid and water

⇒ $\frac{45gm}{1gm/cc}=\frac{35gm}{dgm/cc}$

⇒ $d=\frac{35}{45}gm/cc$

⇒ $d=0.77gm/cc$

Then the density of the liquid is $0.77gm/cc$.

Step 4: Finding the relative density

The relative density of the liquid is given by the formula: $\frac{Densityoftheliquid}{Densityofthewater}$

⇒ The relative density of the liquid is $\frac{0.77gm/cc}{1gm/cc}$.

The relative density of the liquid is $0.77$.