Density Solution

Question

You are asked to prepare a binary mixture of distilled water (dH2O) and lithium metatungstate (LMT) such that the final density of the binary mixture is 2.427 g/cm3. The specific gravity of LMT is 2.95. [Recall that specific gravity is defined as the ratio of a liquid’s density to the density of distilled water.] At 25.0°C, the density of dH2O is 0.997044 g/cm3.

You may assume that all liquids are at 25.0°C.

In order to receive credit, you must show each step of your calculations. Pay particular attention to formulas, units, conversion factors, unit cancellations, and significant figures:

How much of each liquid must you use in order to achieve a final volume of 12.0 ml of a 2.522 g/cm3 density solution?

Answer 1

Let f be the volume fraction of LMT and (1-f) the volume fraction of water. We make the assumption that the volumes add (which they almost certainly do not for miscible liquids). The mass balance for the first part:

fρ_LMT + (1-f)ρ_W = 2.427 g/cm³

you are given density of the water, but density of the LMT is 2.95*density of water to convert it to g/cm³

You can solve for f using algebra and get the volume fraction of each constituent.

The second part, you solve the same thing except you want the mix that gets you to 2.522 g/cm³ (new f, 1-f)

In order to know the volumes, just multiply total volume by f. Don't round until you give an answer and your worst sig figs was the specific density at 3SF.