Question

a matter of density

imagine that you work at a chemical plant. this morning, four different liquid chemicals accidentally spilled into the same tank. luckily, none of the liquids reacted with one another! also, you know the liquids do not dissolve in one another, so they must have settled in the tank in four separate layers. the sides of the tank are made of steel, so you can only see the surface of what’s inside. but you need to remove the red chemical to use in a reaction later this afternoon.

how will you find and remove the red chemical? by finding the chemicals’ different densities, of course!

the following liquids were spilled into the tank:

• a green liquid that has a volume of 48 l and a mass of 36 kg
• a blue liquid that has a volume of 144 l and a mass of 129.6 kg
• a red liquid that has a volume of 96 l and a mass of 115.2 kg
• a black liquid that has a volume of 120 l and a mass of 96 kg

1. calculate the density of each liquid.

green liquid: _______________
blue liquid: _______________
red liquid: _______________
black liquid: _______________

1. determine the order in which the liquids have settled in the tank.

first (bottom): _______________
second: _______________
third: _______________
fourth (top): _______________

Explanation:

Part 1: Calculate the density of each liquid

The formula for density is $
ho = \frac{m}{V}$, where $
ho$ is density, $m$ is mass, and $V$ is volume. We'll calculate the density for each liquid using this formula.

Step 1: Green Liquid

Mass $m = 36$ kg, Volume $V = 48$ L.
Density $
ho = \frac{36}{48} = 0.75$ kg/L.

Step 2: Blue Liquid

Mass $m = 129.6$ kg, Volume $V = 144$ L.
Density $
ho = \frac{129.6}{144} = 0.9$ kg/L.

Step 3: Red Liquid

Mass $m = 115.2$ kg, Volume $V = 96$ L.
Density $
ho = \frac{115.2}{96} = 1.2$ kg/L.

Step 4: Black Liquid

Mass $m = 96$ kg, Volume $V = 120$ L.
Density $
ho = \frac{96}{120} = 0.8$ kg/L.

Part 2: Determine the order of the liquids in the tank

Liquids with higher density will settle at the bottom, and those with lower density will be at the top. We'll order the liquids from highest to lowest density.

From the calculated densities:

• Red liquid: $1.2$ kg/L (highest)
• Blue liquid: $0.9$ kg/L
• Black liquid: $0.8$ kg/L
• Green liquid: $0.75$ kg/L (lowest)

So the order from bottom (first) to top (fourth) is: Red, Blue, Black, Green.

Answer:

s:

1. Densities:

• Green liquid: $\boldsymbol{0.75}$ kg/L
• Blue liquid: $\boldsymbol{0.9}$ kg/L
• Red liquid: $\boldsymbol{1.2}$ kg/L
• Black liquid: $\boldsymbol{0.8}$ kg/L

2. Order in the tank:

• First (bottom): $\boldsymbol{\text{Red liquid}}$
• Second: $\boldsymbol{\text{Blue liquid}}$
• Third: $\boldsymbol{\text{Black liquid}}$
• Fourth (top): $\boldsymbol{\text{Green liquid}}$