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

The density of the unknown liquid is calculated by subtracting the mass of the empty container from the total mass with the liquid, then dividing that mass by the volume of the container determined by the mass of water it holds, resulting in a density of 1.815 g/mL.

Step-by-step explanation:

The student is asking to calculate the density of an unknown liquid. First, we must determine the mass of the liquid alone by subtracting the mass of the empty container from the total mass when filled with the unknown liquid, which is 38.028 g - 17.322 g = 20.706 g. Then, using the density of water at 25°C (0.997048 g/mL) and the container's weight when filled with water (28.699 g), we calculate the volume of the container by subtracting the weight of the empty container from the weight when filled with water: 28.699 g - 17.322 g = 11.377 g. Dividing this mass by the density of water gives us the volume of the container, which is 11.377 g / 0.997048 g/mL = 11.409 mL (rounded to three significant figures). Finally, we calculate the density of the unknown liquid using its mass and the volume of the container: 20.706 g / 11.409 mL = 1.815 g/mL (rounded to three significant figures).

Answer 2

Density of the unknown liquid = 1.82537 g/mL.

Step-by-step 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 = (m_w)/(Volume\ of\ the\ water)\\\\\Rightarrow Volume\ of\ the\ water=\rho* m_w = 0.997048* 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 (m_l)/(Volume\ of\ unknown\ liquid)=(20.706\ g)/(11.343426\ mL)=1.82537\ g/mL.`