# Time to effervescent an effervescent tablet

Say I have an effervescent tablet and I put in water. I thought that if I break the tablet in two halves it would dissolve quicker than with the whole table (without breaking), but it actually takes the same time.

What would be the scientific reason of this?

• Are you sure that the time is exactly the same?! Normally the dissolution rate should be a function of the external area of the tablet (i.e. powder with lots of external area dissolves faster than a tablet). If you break the tablet you create some extra area so it should dissolve faster, but maybe the change in area is not that big so you don't notice it. Could you give use dimensions of the tablet?! – Michiel Apr 25 '13 at 20:53
• michielm thanks for the comment. Why if I break the tablet I create some extra area? – Nobita Apr 25 '13 at 20:55
• Imagine a whole red apple. Looking at it, all you can see is the red of its skin. Now, cut it in half. Suddenly, you can see not only red, but the white of the insides. The volume of the apple is the same whether it is cut or not, but the surface area is not; there is just as much red skin before or after the cut, but the white insides are entirely new and only appear after the cut. Thus the exposed surface area has increased. How does this affect your experiment? If the surface area of the tablet increases, water can attack it from more places at once, so the tablet is eaten up faster. – Nicolau Saker Neto Apr 26 '13 at 3:38

Dissolution in general

Dissolution is normally a function of several aspects of the solid and liquid and one of them is the interfacial area between the solid and the liquid. A common relation for the dissolution rate which is not always exact, but shows all trends/dependencies very well is the following:

$$\frac{\mathrm dm}{\mathrm dt}=A \frac{D}{d}\left(C_\mathrm s-C_\mathrm b\right)$$ where $A$ is the interfacial area, $D$ is the diffusion coefficient of your solid molecules in the liquid, $d$ is the thickness of the solute boundary layer and $C_\mathrm s$ and $C_\mathrm b$ are the concentrations of the solid molecules at surface and in the bulk (this term is the driving force).

Dissolution of a whole or broken tablet

To make a simple calculation for the whole vs. the broken tablet let us do the math. Assuming that we have a disc-like tablet the surface area is 2 times the frontal area $+$ the area of the sides.

$$A=2 A_\mathrm f+A_\mathrm s$$ For the whole tablet $A_\mathrm f=\frac{\pi}{4}D_\mathrm t^2$ and $A_\mathrm s=\pi h D_\mathrm t$

For the broken tablet $A_\mathrm f=\frac{\pi}{4}D_\mathrm t^2$ and $A_\mathrm s=\pi h D_\mathrm t + 2 h D_\mathrm t$

Here I assume that the tablet is cleanly broken in the exact middle of the disc. So you can already see that the surface area is bigger for the broken tablet, but how much will depend on the specifics of the tablet. Rewriting the area we can see how the different aspects of the broken tablet will influence the area: $$A=\pi D_\mathrm t \left[\frac{D_\mathrm t}{2}+h\left(1+\frac{2}{\pi}\right)\right]$$

From this equation it is clear that if $D_\mathrm t \gg h$ the height term doesn't do much and therefore it will not matter much that the tablet is broken.

For a final check: let's assume some typical numbers now. A typical effervescent tablet is about $D_\mathrm t=2\ \mathrm{cm}$ in diameter and $h=3\ \mathrm{mm}$ thick. This will result in the following surface areas for the broken and the whole tablet: $A_\text{whole}=8.2\ \mathrm{cm^2}$ and $A_\text{broken}=9.4\ \mathrm{cm^2}$.

This means that the difference in dissolution rate will only be about $20\ \%$ which is probably hard to notice due to other effects that disturb the comparison. One such effect is that $d$ depends on the amount of stirring which will be different already when you drop the tablets in the glass in a slightly different way (which is unavoidable, because you have 1 broken and 1 whole tablet).

Technically, it should dissolve faster, just like you thought! It will dissolve faster because there is a greater surface area : solution ratio (i.e. the broken edges, which used to be 'in the middle' of the tablet, are now exposed to the water). In general, the more surface area exposed, the faster it will dissolve.

So why aren't you observing a noticeable increase in speed? How big is your tablet? When you break it in half, are the 'broken edges' small (in surface area) compared to the rest of the tablet? Just for fun, try cutting the tablet horizontally through the middle (like you would cut a bread roll). This should significantly increase the surface area and the speed to dissolve.