Why Mass Seems to Disappear When a Reaction Produces Gas

You add calcium carbonate chips to hydrochloric acid in a beaker sitting on a balance. The mixture fizzes, bubbles rise, and the balance reading drops. Has the reaction destroyed some matter?

Before reading on, predict what would happen if you performed the same reaction inside a properly sealed flask. The flask would still produce gas, but its total mass should remain unchanged. The difference is not the chemistry. It is whether matter can escape from the system being weighed.

01The reaction moves atoms; it doesn’t make them disappear

Calcium carbonate, \(\ce{CaCO3}\), reacts with hydrochloric acid, \(\ce{HCl}\), to form calcium chloride, water, and carbon dioxide.

The balanced equation is:

\[ \ce{CaCO3(s) + 2HCl(aq) -> CaCl2(aq) + H2O(l) + CO2(g)} \]

Notice the final product: carbon dioxide, \(\ce{CO2}\), which is a gas.

In an open beaker, this gas can escape into the surrounding air. The calcium chloride remains dissolved in the liquid, and most of the water stays in the beaker.

But the carbon dioxide hasn’t appeared from nowhere. Its atoms were already present in the reactants.

Follow every atom

The balanced equation lets us account for every type of atom on both sides.

The atoms have been rearranged into different substances, but none have been destroyed.

• Calcium ends up in the calcium-containing product, represented by \(\ce{CaCl2(aq)}\).
• Carbon ends up in carbon dioxide, \(\ce{CO2(g)}\).
• Hydrogen and oxygen are accounted for in the water and carbon dioxide.
• Chlorine ends up in the calcium chloride.

The equation tracks the numbers of each type of atom, not the exact molecular pathway by which individual atoms move between products.

So why does the balance reading fall? To answer that, we need to distinguish between the total mass of all the matter involved and the mass of the matter that remains on the balance.

02The system boundary decides what gets counted

A system boundary is an imaginary line around the matter you have chosen to study. It helps you decide which matter is included in your calculation.

For a school investigation, imagine drawing the boundary around the reaction vessel and its contents.

In an open beaker, carbon dioxide crosses the boundary when it escapes. Once it has left the beaker, it is no longer part of the material being weighed.

In a sealed flask, the carbon dioxide remains inside the boundary. It may occupy the space above the liquid, but it is still part of the system.

The crucial difference is whether matter crosses the boundary.

Conservation of mass applies in both cases. The open beaker and sealed flask simply allow different amounts of matter to leave the material being weighed.

03What a balance actually measures

A balance does not identify chemicals or count atoms. It senses the force exerted by the object on the weighing pan and converts that measurement into a mass reading.

The reading includes the mass of the vessel and the material it contains, including gas retained inside a sealed vessel. Gas is not massless.

Suppose a sealed flask contains liquid, unreacted calcium carbonate, and some air. After the reaction, some of the liquid and solid have become calcium chloride, water, and carbon dioxide.

The substances have changed, but if no matter enters or leaves the flask, the total mass has not changed.

The gas still contributes to the mass of the sealed flask. Its pressure may increase, but that does not make its mass disappear.

In the open beaker, carbon dioxide can escape. The mass remaining on the balance then decreases because matter has left the weighed system.

For the usual school calculation, we assume that carbon dioxide is the only significant net mass transfer and that splashing, evaporation, and measurement disturbances are negligible.

A useful distinction: gas produced versus gas lost

These two quantities are not always the same.

• Gas produced is the total amount of carbon dioxide formed by the chemical reaction.
• Gas lost is the amount of carbon dioxide that actually leaves the system being weighed.

Some carbon dioxide can remain in the liquid because it dissolves in water. Some may still be in the gas space inside the vessel when the measurement is taken.

This distinction matters when you compare a measured mass change with the mass predicted by the balanced equation.

If the measured loss is smaller than expected, some gas may not yet have escaped, or the reaction may be incomplete. If the loss is larger than the theoretical carbon dioxide mass, other matter may have escaped as well.

A balance tells you the net mass change of the weighed system. It does not, by itself, tell you exactly which substances caused that change.

06How to run a fair conservation-of-mass investigation

A good experiment needs to separate the chemical reaction from the act of measuring it.

A suitable comparison follows this sequence:

1. Use the same measured quantities of calcium carbonate and hydrochloric acid in both trials.
2. Keep the reactants separate until the initial mass has been recorded.
3. For the open trial, mix the reactants in an open vessel and allow the reaction to proceed.
4. For the sealed trial, use a teacher-approved, pressure-rated apparatus. Seal it before mixing, then mix the reactants without opening it.
5. Wait for the reaction to finish, then record the final mass of each complete apparatus.

Never seal an ordinary glass flask that is not designed to withstand the pressure generated by a gas-producing reaction.

For each trial, compare the initial and final readings rather than comparing the absolute masses of different apparatuses.

If the experiment behaves as expected, the open vessel will show a mass decrease, while the sealed system will show no significant change within the balance’s measurement uncertainty.

What can go wrong with the results?

The ideal model assumes that only carbon dioxide leaves the open vessel. Real experiments can be less tidy.

• A mass decrease smaller than predicted may indicate that some carbon dioxide remains dissolved in the liquid, gas is still being released, or the reaction is incomplete.
• A mass decrease larger than predicted may indicate that water evaporated, acid-containing droplets escaped, or another source of mass loss was present.
• A significant mass decrease in a supposedly sealed system suggests a leak, another form of matter transfer, or a measurement problem.

These results do not overturn conservation of mass. They tell you to check the assumptions behind your experiment.

07Questions and solutions

Question 1

A student reacts 0.500 g of calcium carbonate with excess hydrochloric acid. Assume the reaction goes to completion and use \(M(\ce{CaCO3})=100.1\text{ g mol}^{-1}\) and \(M(\ce{CO2})=44.0\text{ g mol}^{-1}\).

Calculate the theoretical mass of carbon dioxide produced. State the expected mass change for an open vessel if all the gas escapes, and for a properly sealed system.

Solution 1

The theoretical carbon dioxide mass is approximately 0.220 g. The open vessel should lose 0.220 g under the stated assumptions, while the sealed system should show no change in total mass.

The balanced equation gives a 1:1 mole ratio between calcium carbonate and carbon dioxide.

First, calculate the amount of calcium carbonate:

\[ \begin{aligned} n(\ce{CaCO3})&=\frac{0.500}{100.1}\\\ &=0.004995\text{ mol} \end{aligned} \]

Therefore,

\[ n(\ce{CO2})=0.004995\text{ mol} \]

The carbon dioxide mass is

\[ \begin{aligned} m(\ce{CO2})&=nM\\\ &=0.004995\times44.0\\\ &=0.220\text{ g} \end{aligned} \]

In the open vessel, this gas leaves the weighed system, so the expected mass change is \(-0.220\text{ g}\).

In the sealed system, the same carbon dioxide is produced but remains inside the vessel. Its formation does not change the total mass, so the expected mass change is \(0\text{ g}\).

Question 2

A student reacts 1.50 g of calcium carbonate with excess hydrochloric acid in an open beaker. The balance reading decreases by 0.73 g.

Assume all the calcium carbonate reacts. The theoretical carbon dioxide mass is approximately 0.66 g.

Explain why the measured mass decrease cannot be explained by carbon dioxide alone. Give two plausible causes of the extra apparent mass loss, and explain why conservation of mass has not been disproved.

Solution 2

The measured decrease is about 0.07 g greater than the theoretical carbon dioxide mass, so another mass transfer or a measurement problem must be considered.

The expected carbon dioxide mass is

\[ \begin{aligned} m(\ce{CO2})&=\frac{1.50}{100.1}\times44.0\\\ &=0.659\text{ g}\\\ &\approx0.66\text{ g} \end{aligned} \]

The difference between the measured loss and the predicted carbon dioxide mass is

\[ \begin{aligned} \Delta m_{\text{extra}}&=0.73-0.659\\\ &=0.071\text{ g} \end{aligned} \]

Two plausible causes are:

• Water evaporated from the open beaker, adding to the mass lost.
• Small droplets of liquid escaped during vigorous bubbling, carrying dissolved substances with them.

A balance disturbance or other measurement error could also explain the discrepancy.

The key constraint is that 1.50 g of calcium carbonate cannot produce more than approximately 0.66 g of carbon dioxide under the stated reaction conditions. The additional decrease must be explained by something beyond the carbon dioxide predicted by the equation.

The law of conservation of mass still holds for all the matter involved. The experiment simply did not measure carbon dioxide as the only mass leaving the system.

Question 3

Two rigid, sealed flasks contain equal amounts of calcium carbonate and excess hydrochloric acid. The reactants are initially separated inside each flask, and the flasks are sealed before mixing.

Flask A has a gas headspace of 100 mL, while flask B has a gas headspace of 200 mL. Both reactions go to completion at the same temperature. For this question, assume all the carbon dioxide remains gaseous and behaves ideally.

Which flask has the higher carbon dioxide partial pressure after the reaction? Explain why this does not mean it contains more carbon dioxide or has gained more mass.

Solution 3

Flask A has twice the carbon dioxide partial pressure of flask B, but both flasks produce the same amount of carbon dioxide and retain their original total mass.

The ideal gas equation for the carbon dioxide is

\[ pV=nRT \]

where \(p\) is its partial pressure, \(V\) is the headspace volume, \(n\) is the amount of carbon dioxide in moles, \(R\) is the gas constant, and \(T\) is the absolute temperature.

Rearranging gives

\[ p=\frac{nRT}{V} \]

Both flasks have the same \(n\) because they contain the same amount of calcium carbonate and the reaction goes to completion. They also have the same temperature.

Therefore, the carbon dioxide partial pressure is inversely proportional to the headspace volume:

\[ \frac{p_A}{p_B}=\frac{V_B}{V_A} =\frac{200}{100}=2 \]

Flask A has the smaller headspace, so the same amount of gas occupies half the volume and exerts twice the carbon dioxide partial pressure.

Pressure describes the gas’s effect on the walls of the container. It is not a direct measurement of total mass. Both flasks retain all their matter, so each should have an unchanged total mass reading. Their total pressures also include the contribution from any trapped air.

Question 4

A student reacts 2.00 g of calcium carbonate with excess hydrochloric acid. The theoretical carbon dioxide mass is 0.88 g.

The student obtains these results:

The balance uncertainty is approximately \(\pm 0.01\text{ g}\). Both reactions go to completion, and no liquid is visibly spilled.

Evaluate the results. Does the open trial prove that only carbon dioxide left the system? What does the sealed trial suggest, and how should the investigation be improved?

Solution 4

The open result is consistent with the predicted carbon dioxide loss, but it does not prove that carbon dioxide was the only matter to leave. The sealed trial shows a mass decrease too large to attribute to the stated balance uncertainty alone, suggesting that the system was not behaving as a perfectly closed system or that another experimental problem occurred.

For the open trial, the measured decrease is

\[ 155.00-154.13=0.87\text{ g} \]

This is close to the theoretical value of 0.88 g. The difference of 0.01 g is consistent with the stated measurement uncertainty and rounding.

However, agreement with the predicted value is not proof that only carbon dioxide escaped. For example, some carbon dioxide might remain dissolved while a small amount of water evaporates. These effects could partially offset each other, producing a reading close to the theoretical value.

For the sealed trial, the measured decrease is

\[ 231.80-231.68=0.12\text{ g} \]

This is much larger than the stated uncertainty. If the vessel were genuinely sealed, no liquid or other matter escaped, and measurement conditions were stable, the expected mass change would be zero.

The result suggests a leak, an imperfect seal, another form of mass transfer, or a measurement problem. It does not show that conservation of mass has failed.

To improve the investigation, use a pressure-rated apparatus with a verified seal, keep the reactants separated until the initial weighing, prevent liquid from escaping, and use the same controlled weighing procedure for both trials. Repeat the measurements and compare the results with the balance’s uncertainty.

Question 5

A student places 1.00 g of calcium carbonate and excess hydrochloric acid inside a rigid flask. The reactants are separated in an inner container. The flask is sealed and weighed, the reactants are mixed without opening the flask, and the reaction is allowed to finish.

The sealed flask has exactly the same mass reading before and after the reaction. The student then removes the stopper while the flask remains on the balance. The reading decreases by 0.03 g and eventually stabilises. No liquid spills.

Assume all the calcium carbonate reacts, no other reaction produces carbon dioxide, and \(M(\ce{CaCO3})=100.1\text{ g mol}^{-1}\) and \(M(\ce{CO2})=44.0\text{ g mol}^{-1}\).

(a) Calculate the theoretical mass of carbon dioxide produced.

(b) A student claims that only 0.03 g of carbon dioxide was produced because that is the observed mass decrease after opening the flask. Explain why this conclusion is incorrect. Your explanation must account for the gas inside the sealed flask, the entry of air when the stopper is removed, and carbon dioxide that may remain dissolved in the liquid.

(c) Explain why it would also be incorrect to subtract 0.03 g from the theoretical carbon dioxide mass and conclude that the difference is the mass of carbon dioxide still inside the flask. Describe a measurement that could help determine how much carbon dioxide remains dissolved.

Solution 5

(a) The reaction produces approximately 0.440 g of carbon dioxide. (b) The 0.03 g decrease after opening is a net mass change, not the total mass of carbon dioxide produced. (c) The difference between 0.440 g and 0.03 g cannot be treated as the mass of carbon dioxide remaining inside, because opening the flask allows air to enter as well as gas to leave.

Step 1: Calculate the theoretical amount of carbon dioxide.

The balanced equation gives a 1:1 mole ratio between calcium carbonate and carbon dioxide.

\[ \begin{aligned} n(\ce{CaCO3})&=\frac{1.00}{100.1}\\\ &=0.00999\text{ mol} \end{aligned} \]

Since all the calcium carbonate reacts,

\[ n(\ce{CO2})=0.00999\text{ mol} \]

Therefore,

\[ \begin{aligned} m(\ce{CO2})&=nM\\\ &=0.00999\times44.0\\\ &=0.440\text{ g} \end{aligned} \]

This is the theoretical mass of carbon dioxide formed by the reaction.

Step 2: Explain the unchanged reading while the flask is sealed.

The carbon dioxide is produced inside the flask, so it remains part of the weighed system. Some occupies the headspace, and some may dissolve in the liquid.

The reaction changes the chemical substances present, but no matter crosses the sealed boundary. Therefore, the total mass remains unchanged.

Step 3: Explain the 0.03 g decrease after opening.

Once the stopper is removed, the boundary is no longer closed to matter. Carbon dioxide-rich gas can leave the flask, while surrounding air enters to occupy some of the space it vacates.

The balance records the net mass change resulting from matter leaving and entering the weighed system. It does not simply measure the mass of carbon dioxide that was produced during the reaction.

Furthermore, some carbon dioxide may remain dissolved in the liquid after the reading stabilises. The amount dissolved depends on conditions such as temperature and the composition of the solution.

Consequently, the observed decrease of 0.03 g does not mean that only 0.03 g of carbon dioxide was formed. The reaction produced approximately 0.440 g under the stated assumptions, even though the change in the balance reading after opening was much smaller.

Step 4: Explain why the remaining mass cannot be found by simple subtraction.

It would be tempting to calculate

\[ 0.440-0.030=0.410\text{ g} \]

and conclude that 0.410 g of carbon dioxide remains inside the flask. That conclusion is not justified.

The 0.030 g is a net mass change, affected by both outgoing gas and incoming air. It is not necessarily the mass of carbon dioxide that escaped. Some carbon dioxide may also remain dissolved in the liquid, so the gas that leaves the headspace is not necessarily all the carbon dioxide produced.

To measure the dissolved carbon dioxide, a separate controlled experiment could collect the headspace gas and then quantitatively release the remaining dissolved carbon dioxide into a calibrated gas collector. The additional carbon dioxide collected from the liquid would indicate how much had remained dissolved, subject to the accuracy of the collection method.

The central lesson is that conservation of mass applies to the complete set of matter being considered. A balance reading only tells you the mass change of the material it weighs, so you must establish the system boundary before interpreting that change.

Once you can separate the mass of gas produced from the mass that actually escapes, you can use balanced equations to calculate theoretical yields and investigate why measured yields differ. That is the next step towards understanding limiting reagents, gas collection, and percentage yield.