Animated Solution for Chemistry - Basic Concepts in Chemistry: A $10\text{ mg}$ effervescent tablet containing sodium bicarbonate and oxalic acid releases $0.25\text{ mL}$ of ${\text{CO}}_2$ at $T=298.15\text{ K}$ and $p=1\text{ bar}$. If molar volume of ${\text{CO}}_2$ is $25.0\text{ L}$ under such condition, what is the percentage of sodium bicarbonate in each tablet? [Molar mass of ${\text{NaHCO}}_3=84{\text{ g mol}}^{-1}$]

Have you ever dropped an effervescent tablet into a glass of water and watched it fizz vigorously? That satisfying bubbling is actually a fascinating chemical reaction happening right before your eyes! In this problem, we are going to play the role of a chemical detective. We are given a $10\text{ mg}$ tablet that releases exactly $0.25\text{ mL}$ of ${\text{CO}}_2$ gas. Our mission? To figure out exactly what percentage of that tablet is pure sodium bicarbonate (${\text{NaHCO}}_3$).

I know stoichiometry can sometimes feel like a maze of numbers, but let's take a breath and break it down logically. We will connect the volume of the gas released to the mass of the solid reactant using the universal language of chemistry: the mole.

The Mole Concept

The first thing we need to do is figure out how much ${\text{CO}}_2$ was actually produced. We are given the volume of the gas, but chemical equations don't speak in milliliters; they speak in moles.

To translate volume into moles, we use the concept of molar volume. The problem generously tells us that under these specific conditions ($T=298.15\text{ K}$ and $p=1\text{ bar}$), one mole of ${\text{CO}}_2$ occupies $25.0\text{ L}$.

Therefore, the number of moles of ${\text{CO}}_2$ is simply the given volume divided by the molar volume. But watch out for the units! We must convert our given volume from milliliters to liters to match the molar volume.

This tiny number represents the exact amount of carbon dioxide molecules that bubbled out of the water.

Now that we know how much gas was produced, we need to trace it back to the source: the sodium bicarbonate in the tablet. This is where the balanced chemical equation becomes our map.

The reaction between sodium bicarbonate and oxalic acid is:

Look closely at the stoichiometric coefficients. For every $2\text{ moles}$ of ${\text{NaHCO}}_3$ that react, exactly $2\text{ moles}$ of ${\text{CO}}_2$ are produced. This is a beautiful $1:1$ ratio!

Because the ratio is $1:1$, the moles of sodium bicarbonate must be exactly equal to the moles of carbon dioxide we just calculated.

We are almost there! We know the moles of sodium bicarbonate, but the question asks for a percentage by mass. So, our next step is to convert these moles back into a tangible mass.

We do this by multiplying the moles by the molar mass of ${\text{NaHCO}}_3$, which is given as $84\text{ g/mol}$.

To make this number easier to work with, let's convert it to milligrams, since the total mass of the tablet is given in milligrams.

Finally, to find the percentage purity of the tablet, we divide the mass of the pure sodium bicarbonate by the total mass of the tablet and multiply by $100$.

Isn't it amazing how we can use the volume of a few bubbles to precisely determine the chemical composition of a solid tablet? That is the true power of stoichiometry!