Question

A vessel of `50*g` mass was filled with water, and the mass of the vessel and its content were `125*g`. The water was emptied, and the vessel was filled with an unknown liquid, and the mass of the vessel and it contents was `110*g`. Can you address?

`"(i) what was the density of the unknown liquid;"`
`"(ii) what was the relative density of the unknown liquid?"`

Answer 1

We can infer IMMEDIATELY that the volume of the vessel is `75*mL`. Why?

Explanation:

Because we filled the vessel with `(125-50)*g=75*g` water, which has a VOLUME of `75*mL`.

When it was filled with an unknown liquid, the volume of the liquid is still `75*mL`, but the MASS of the unknown liquid was `110*g-50*g=60*g`, and thus its density, `rho`, was `"mass"/"volume"` `=` `(60*g)/(75*mL)=0.80*g*mL^-1`.

And thus `rho_"relative"=rho_"substance"/rho_"water"=(0.80*g*mL^-1)/(1.00*g*mL^-1)=0.80`, a dimensionless quantity as required.

Do you agree that this should float on water if it is immiscible with water......?

`rho_"n-pentane"=0.63*g*mL^-1`........

`rho_"n-hexane"=0.65*g*mL^-1`........

`rho_"n-heptane"=0.68*g*mL^-1`........

`rho_"n-octane"=0.70*g*mL^-1`........

`rho_"n-butyl chloride"=0.89*g*mL^-1`........

`rho_"isopropyl chloride"=0.862*g*mL^-1`........

I list the densities of some common water immiscible solvents for comparison.

On the other hand, `rho_"ethyl alcohol"=0.79*g*mL^-1`........Its density is certainly consistent (within experimental error) with that of the given liquid. Why can you argue that the unknown solvent is NOT `"ethyl alcohol"`?