Laws of Mass and Stoichiometric Relationships

We dissolve an effervescent tablet of $3\ \text{g}$ in a beaker of $100\ \text{g}$ of water. When the bubbling stops, the whole system weighs $102,5\ \text{g}$. Observe the diagram of the process:

1. a) What mass of gas has escaped into the air?
2. b) Does this result contradict the law of conservation of mass? Reason your answer.

When a candle is weighed on a balance before and after being left to burn for a while, we find that the whole system has lost mass. The diagram shows what happens:

1. a) Does this mean that matter has been destroyed? Explain what has actually happened.
2. b) How would you design the experiment to check that the total mass is conserved?

In a kiln, $10\ \text{g}$ of calcium carbonate decomposes due to heat, producing $5,6\ \text{g}$ of calcium oxide and $4,4\ \text{g}$ of carbon dioxide, as summarised in the diagram:

1. a) Check that the law of conservation of mass is obeyed.
2. b) If $25\ \text{g}$ of calcium carbonate decomposes, what mass of each product will be obtained? Which second law of chemical combination are you applying?

In a laboratory, two samples of copper(II) oxide from different sources are analysed. Sample A contains $3,97\ \text{g}$ of copper and $1,00\ \text{g}$ of oxygen; Sample B contains $11,91\ \text{g}$ of copper and $3,00\ \text{g}$ of oxygen.

1. a) Calculate the ratio $\frac{\text{masa de cobre}}{\text{masa de oxígeno}}$ in each sample.
2. b) Could they be the same compound? Which law of chemical combination guarantees this?

A sample of $15,9\ \text{g}$ of copper(II) oxide contains $12,7\ \text{g}$ of copper and $3,2\ \text{g}$ of oxygen.

1. a) What mass of oxygen will be combined with $25,4\ \text{g}$ of copper in another sample of the same oxide?
2. b) What will be the total mass of that second sample?

A company buys industrial copper(II) oxide and suspects that it arrives with impurities. Pure oxide combines copper and oxygen in the ratio of $63,5\ \text{g}$ of copper for every $16\ \text{g}$ of oxygen. Analysis of a $10,0\ \text{g}$ sample of the product received shows that it contains only $7,6\ \text{g}$ of copper.

1. a) Calculate what mass of copper a sample of $10,0\ \text{g}$ of pure copper(II) oxide should contain.
2. b) Is the product received pure? Justify your answer using the law of definite proportions.
3. c) Assuming that the impurity does not contain copper, estimate the purity of the product as a percentage.

Carbon forms two gaseous oxides. In one of them, $3\ \text{g}$ of carbon combines with $4\ \text{g}$ of oxygen; in the other, $3\ \text{g}$ of carbon combines with $8\ \text{g}$ of oxygen, as shown in the figure:

1. a) Calculate the ratio between the two masses of oxygen that combine with the same mass of carbon.
2. b) Which law of chemical combination do these data illustrate, and who stated it?

Nitrogen forms several oxides. Fixing the mass of nitrogen at $14\ \text{g}$, the masses of combined oxygen are $16\ \text{g}$ in nitrogen monoxide, $32\ \text{g}$ in nitrogen dioxide, and $40\ \text{g}$ in dinitrogen pentoxide.

1. a) Express the ratio $16 : 32 : 40$ as a ratio of simple integers.
2. b) State the law of chemical combination that these data predict and explain its meaning.

Chlorine forms four oxides: $\text{Cl}_2\text{O}$, $\text{Cl}_2\text{O}_3$, $\text{Cl}_2\text{O}_5$, and $\text{Cl}_2\text{O}_7$ (atomic masses: $\text{Cl} = 35,5\ \text{u}$; $\text{O} = 16\ \text{u}$).

1. a) Calculate the mass of oxygen that combines with $71\ \text{g}$ of chlorine in each of the four oxides.
2. b) Check that these masses are in the ratio of simple integers $1 : 3 : 5 : 7$.
3. c) Predict what mass of oxygen would combine with $71\ \text{g}$ of chlorine in a hypothetical oxide $\text{Cl}_2\text{O}_9$ and state in your own words the law you have used.

The industrial synthesis of ammonia is summarised as follows: $28\ \text{g}$ of nitrogen reacts with $6\ \text{g}$ of hydrogen to yield $34\ \text{g}$ of ammonia.

1. a) What mass of hydrogen is needed to react with $56\ \text{g}$ of nitrogen?
2. b) What mass of ammonia will then be produced?
3. c) State which two laws of chemical combination you have applied and in which part.

$10\ \text{g}$ of hydrogen and $64\ \text{g}$ of oxygen are introduced into a closed reactor to produce water. The stoichiometric ratio by mass is $1\ \text{g}$ of hydrogen for every $8\ \text{g}$ of oxygen.

1. a) Determine which reactant is used up first and justify your answer with a calculation.
2. b) Calculate the mass of water formed and the mass of the remaining reactant.
3. c) Check that the total mass inside the reactor before and after the reaction is the same. Which law requires this?

In a lime kiln, $200\ \text{g}$ of limestone (pure calcium carbonate) is heated to obtain $112\ \text{g}$ of quicklime (calcium oxide) and $88\ \text{g}$ of carbon dioxide.

1. a) Check that mass is conserved in the process.
2. b) Express the stoichiometric mass ratio calcium carbonate : calcium oxide : carbon dioxide using integers.
3. c) Predict what mass of quicklime and carbon dioxide $500\ \text{g}$ of limestone will produce, indicating which two laws of chemical combination make this prediction possible.