Question

When equal volumes of two substances are mixed their density?

Answer 1

The density of the mixture will equate to the mass of the mixture divided by the volume of the mixture, i.e.

Pmix=MmixVmixPmix=MmixVmix

If the mass of each substance is mm, then (assuming that the mixing does not lead to a chemical reaction that, say, produces a gas), then Mmix=2mMmix=2m

What is VmixVmix? Well, as has already been mentioned by Leif Neland, adding a volume V1 of one substance to a volume V2 of another substance does not always result in a mixture with a volume equal to V1+V2. If this is the case with your two substances, then we can go no further than saying

Pmix=2mVmixPmix=2mVmix

But what is there is no change in volume?

Well, we know that P1=mV1P1=mV1, so V1=mP1V1=mP1

Likewise, V2=mP2V2=mP2

Thus Vmix=mP1+mP2=mP1+P2P1.P2Vmix=mP1+mP2=mP1+P2P1.P2

Thus Pmix=2mm(P1+P2)P1.P2=2m.P1.P2P1+P2=2P1.P2P1+P2Pmix=2mm(P1+P2)P1.P2=2m.P1.P2P1+P2=2P1.P2P1+P2