Question

An empty container weighs 17.322 g. When filled with water at 25°C, it weighs 28.699 g. When filled with an unknown liquid, it weighs 38.028 g including the container. What is the density of the unknown liquid? (Density of water = 0.997048 g/mL)

Answer 1

Answer:

Density of the unknown liquid = 1.82537 g/mL.

Explanation:

Given:

• Mass of the empty container, m = 17.322 g.

• Mass of the container with the water at 25°C = 28.699 g.

• Mass of the container with the unknown liquid = 38.028 g.

• Density of the water, $\rm \rho=0.997048\ g/mL.$

Assumptions:

• Mass of the water at 25°C that fills the container = $\rm m_w$

• Mass of the unknown liquid that fills the container = $\rm m_l$

Therefore,

$\rm m+m_w = 28.699\ g\\17.322\ g+m_w = 28.699\ g\\m_w = 28.699-17.322=11.377\ g.\\\\\rho = \dfrac{m_w}{Volume\ of\ the\ water}\\\\\Rightarrow Volume\ of\ the\ water=\rho\times m_w = 0.997048\times 11.377=11.343426\ mL.$

The volume occupied by the unknown liquid should also be same.

Volume of unknown liquid = 11.343426 mL.

Also,

$\rm m+m_l=38.028\ g\\m_l=38.028-m=38.028-17.322=20.706\ g.$

Density of the unknown liquid = $\rm \dfrac{m_l}{Volume\ of\ unknown\ liquid}=\dfrac{20.706\ g}{11.343426\ mL}=1.82537\ g/mL.$