Exercises: Law of definite proportions (Proust)

Complete the sentence with the missing words: "When two or more elements combine to form a specific $\dots$, they always do so in the same proportion by $\dots$, regardless of the amount of $\dots$ or its origin."

In water, hydrogen and oxygen combine in the ratio of $1\ \text{g}$ of hydrogen for every $8\ \text{g}$ of oxygen. How many grams of oxygen will combine with $4\ \text{g}$ of hydrogen?

To form carbon dioxide, carbon and oxygen combine in the ratio of $3\ \text{g}$ of carbon for every $8\ \text{g}$ of oxygen. What mass of oxygen do you need to completely burn $9\ \text{g}$ of carbon?

One water sample contains $2\ \text{g}$ of hydrogen and $16\ \text{g}$ of oxygen; another sample contains $5\ \text{g}$ of hydrogen and $40\ \text{g}$ of oxygen. The figure compares the composition of the two samples.

Calculate the ratio between hydrogen and oxygen in each sample and explain whether they could be the same compound.

One sample contains $3\ \text{g}$ of carbon and $8\ \text{g}$ of oxygen, and another contains $3\ \text{g}$ of carbon and $4\ \text{g}$ of oxygen. Could they be the same compound? Justify your answer using Proust's law (the law of definite proportions).

Will $6\ \text{g}$ of carbon combine completely with $16\ \text{g}$ of oxygen to form carbon dioxide, with nothing left over? What mass of carbon dioxide will form? (Remember: the ratio is $3\ \text{g}$ of carbon for every $8\ \text{g}$ of oxygen.)

We analyze distilled water from a laboratory and collected, purified rainwater. In what ratio do hydrogen and oxygen combine in each? What does Proust's law say about the origin of the samples?

If $1\ \text{g}$ of hydrogen reacts exactly with $8\ \text{g}$ of oxygen, what mass of water is formed? What other law of chemical reactions did you need besides Proust's law?

In a sealed container, we place $10\ \text{g}$ of hydrogen and $64\ \text{g}$ of oxygen and cause them to react (the combination ratio is $1:8$). The figure shows the container before the reaction.

1. a) Does all the hydrogen react?
2. b) What mass of water is formed?
3. c) Is there any gas left over? What mass?

We burn $12\ \text{g}$ of carbon with $40\ \text{g}$ of oxygen (the combination ratio is $3:8$).

1. a) How much oxygen is consumed?
2. b) What mass of carbon dioxide is formed?
3. c) What mass of oxygen remains unreacted?

Calcium and oxygen combine in the ratio $5:2$ to form quicklime (calcium oxide).

1. a) What mass of calcium combines with $16\ \text{g}$ of oxygen?
2. b) What mass of quicklime is obtained?

A laboratory analyzes two samples of an iron oxide. Sample A contains $14\ \text{g}$ of iron and $6\ \text{g}$ of oxygen; sample B contains $21\ \text{g}$ of iron and $9\ \text{g}$ of oxygen. Calculate the ratio for each and decide if they are the same compound.

We completely decompose $90\ \text{g}$ of water into its elements (ratio $1:8$ between hydrogen and oxygen). What mass of hydrogen and what mass of oxygen are obtained?

In ammonia, nitrogen and hydrogen combine in the ratio $14:3$.

1. a) What mass of hydrogen combines exactly with $28\ \text{g}$ of nitrogen?
2. b) What mass of ammonia is formed?

Copper can form two different oxides. In one sample, $8\ \text{g}$ of copper combine with $2\ \text{g}$ of oxygen; in another sample, $8\ \text{g}$ of copper combine with $1\ \text{g}$ of oxygen. The figure compares the composition of the two samples.

Is it the same oxide? How do you know?

Magnesium and oxygen combine in the ratio $3:2$ when forming magnesium oxide. If we analyze $20\ \text{g}$ of magnesium oxide, what mass of magnesium and what mass of oxygen does it contain?

We mix $16\ \text{g}$ of hydrogen with $100\ \text{g}$ of oxygen and trigger the reaction (ratio $1:8$).

1. a) What mass of each gas reacts?
2. b) What mass of water is formed?
3. c) What mass of hydrogen is left over?

We analyze three samples of "iron oxide". Sample A contains $14\ \text{g}$ of iron and $6\ \text{g}$ of oxygen; sample B, $14\ \text{g}$ of iron and $4\ \text{g}$ of oxygen; sample C, $21\ \text{g}$ of iron and $9\ \text{g}$ of oxygen.

1. a) Calculate the iron:oxygen ratio for each sample.
2. b) Which of them are the same compound?
3. c) Explain why iron can give rise to more than one different oxide.

In a first experiment, we form water by combining $2\ \text{g}$ of hydrogen with $16\ \text{g}$ of oxygen. In another experiment, we decompose $9\ \text{g}$ of water and obtain $1\ \text{g}$ of hydrogen and $8\ \text{g}$ of oxygen.

1. a) Verify that both results comply with the law of definite proportions.
2. b) Explain the difference between the two experiments (synthesis and analysis) and reason why the ratio is the same in both.

A student claims: "If I add twice as much oxygen, the water that forms will contain twice as much oxygen." To test this, we combine $4\ \text{g}$ of hydrogen with $64\ \text{g}$ of oxygen (twice as much as necessary).

1. a) Calculate the mass of water formed and the mass of oxygen left over.
2. b) Use Proust's law (the law of definite proportions) to explain why the student is mistaken.

In a first experiment, $4\ \text{g}$ of copper combine exactly with $1\ \text{g}$ of oxygen. In a second experiment, we start with twice as much copper.

1. a) What mass of oxygen will combine with $8\ \text{g}$ of copper?
2. b) What mass of oxide is obtained in each experiment?
3. c) Does the combination ratio depend on the amount of sample used? Justify your answer.

Carbon and oxygen can form two different gases. In sample A, there are $6\ \text{g}$ of carbon and $8\ \text{g}$ of oxygen; in sample B, there are $6\ \text{g}$ of carbon and $16\ \text{g}$ of oxygen. The figure shows the model of each molecule.

1. a) Calculate the carbon:oxygen ratio for each sample.
2. b) Are they the same compound?
3. c) Given that one of the gases is carbon monoxide (highly toxic) and the other is carbon dioxide, explain why Proust's law (the law of definite proportions) allows us to distinguish between them even though they are made of the same elements.

A class measures the composition of water and obtains $10.2\ \text{g}$ of hydrogen and $79.8\ \text{g}$ of oxygen.

1. a) Calculate the oxygen/hydrogen ratio (to one decimal place) and compare it with the theoretical ratio $8:1$.
2. b) Should we conclude that Proust's law fails? Reason your answer.
3. c) Point out two possible causes for the slight discrepancy with the theoretical value.

A laboratory receives $250\ \text{g}$ of a white mineral that the supplier claims is pure calcium oxide (calcium:oxygen ratio $5:2$). Analysis reveals $175\ \text{g}$ of calcium and $75\ \text{g}$ of oxygen.

1. a) Check whether the mineral could be pure calcium oxide.
2. b) What mass of oxygen should accompany $175\ \text{g}$ of calcium if it were?
3. c) Propose an explanation for the result of the analysis.