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Recently in Chemistry 101 we learned about $M_1V_1=M_2V_2$, where $M$ is the molarity of the two mixtures and $V$ is their respective volumes.

The first thing that popped into my mind when I saw this formula is, “Hey, that reminds me of Boyle’s Law from high school physics - $P_1V_1=P_2V_2$ - the relationship between the volumes of a gas at different pressures.”

Is it just a coincidence that these two formulae look the same, or is there a connection between the pressure variable in Boyle’s Law and the molarity variable in the first equation? Are there other formulae which are structured similarly which are connected?

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Yes, they are related. The first comes directly from the conservation of number of moles of the solute in a dilution,

$$n_1 = n_2 $$

Since $n = MV$,

$$M_1 V_1 = M_2 V_2$$

The second is related to the conservation of the total number of moles in an isothermal compression or expansion,

$$n_1 = n_2$$

Using the ideal gas law $n = pV/RT$,

$$\frac{P_1 V_1}{R T} = \frac{P_2 V_2}{R T}$$

Or $P_1 V_1 = P_2 V_2$.

Again, both are related to the conservation of moles (which by the way, isn't an universal law, since it's broken in trivial situations like the event of a chemical reaction), although the first one refers to solute only and the second to total number of moles.

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  • $\begingroup$ That’s a great way to look at it, thanks! Are there any other formulae that relate to conservation of moles in this fashion? $\endgroup$ – DonielF Oct 16 '19 at 17:19

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