Laws of Chemical Combination

The laws of chemical combination describe the basic principles obeyed by interacting atoms and molecules, interactions that can include many different combinations that happen in many different ways. This amazing diversity of interactions allows for an astounding variety of chemical reactions and compounds. Spontaneous chemical reactions happen constantly, shaping the world around us, while humans engineer specific reactions to our benefit and attempt to curb reactions that hurt us. Though chemical reactions can be as complex as they are numerous, they are all fundamentally governed by these same guiding laws of chemical combination, which lay the groundwork for analysis of chemical reactions. They give a mathematical formulation and allow predictability given initial conditions. They are the launch pad from which we jump off to creating all sorts of wild compounds and phenomena. And while chemistry is still difficult and intricate, with the laws of chemical combination on our side, we can begin to make some headway.

The law of conservation of mass states that the net change in mass of the reactants and products before and after a chemical reaction is zero. This means mass can neither be created nor destroyed. In other words, the total mass in a chemical reaction remains constant.

This law was formulated by Antoine Lavoisier in 1789. It was later found to be slightly inaccurate, as in the course of chemical reactions mass can interconvert with heat and bond energy. However, these losses are very small, several orders of magnitude smaller than the mass of the reactants, so that this law is an excellent approximation.

Does the following chemical reaction obey the law of conservation of mass?

\[\ce{Ca(OH)2 + CO2 -> CaCO3 + H2O}\]

The masses of \(\ce{Ca}\), \(\ce O\), \(\ce H\), and \(\ce C\) are \(40\text{u}, 16\text{u}, 1\text{u},\) and \(12\text{u},\) respectively.

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Since they obey the law of conservation of mass, the answer is yes. Let's verify it. The molecular masses are

\[\begin{array}{rrlrl} \ce{Ca(OH)2}: &40+32+2 &= &74 \\ \ce{CO2}: &12+32&=&44 \\ \ce{CaCO3}: &40+12+48&=&100\\ \ce{H2O}: &2+16&=&18&. \end{array}\]

Substituting these values into the equation,

\[\begin{align} 74+44 &= 100+18\\ 118&=118.\ _\square \end{align}\]

The law of constant proportions states that when a compound is broken, the masses of the constituent elements remain in the same proportion. Or, in a chemical compound, the elements are always present in definite proportions by mass.

This means each compound has the same elements in the same proportions, regardless of where the compound was obtained, who prepared it, or its mass.

This law was formulated and proven by Joseph Louis Proust in 1799.

A person living in Australia sent a \(100\text{ ml}\) sample of \(\ce{CaCO3}\)(calcium carbonate) to a person living in India. The person living in India made his own sample of \(200\text{ ml}\) and compared it to his friend's sample. Which of the two compounds has a greater ratio of \(\ce{Ca}:\ce{C}?\)

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Both contain equal ratios of \(\ce{Ca}\) and \(\ce C\). This is guaranteed by the law of constant proportions. \(_\square\)

The law of multiple proportions states that when two elements form two or more compounds between them, the ratio of the masses of the second element in each compound can be expressed in the form of small whole numbers.

This law was proposed by John Dalton, and it is a combination of the previous laws.

Carbon combines with oxygen to form two different compounds (under different circumstances). One is the most common gas \(\ce{CO2}\) and the other is \(\ce{CO}\). Do they obey the law of multiple proportions?

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Yes, they do obey the law of multiple proportions. Let's verify it.

We know that the mass of carbon is \(12\text{ u}\) and the mass of oxygen is \(16\text{ u}\).
So, we can say that \(12\text{ g}\) of carbon combines with \(32\text{ g}\) of oxygen to form \(\ce{CO2}\).
Similarly, \(12\text{ g}\) of carbon combines with \(16\text{ g}\) of oxygen to form \(\ce{CO}\).

So, the ratio of oxygen in the first and second compound is \(2:1=\frac{32}{16}= 2,\) which is a whole number. \(_\square\)

The law of reciprocal proportions states that when two different elements combine with the same quantity of the third element, the ratio in which they will do so will be the same or a multiple of the proportion in which they combine with each other.

This law was proposed by Jeremias Ritcher in 1792.

Oxygen and sulfur react with copper to create copper oxide and copper sulfide, respectively. Sulfur and oxygen also react with each other to form \(\ce{SO2}.\) Therefore,

\[\begin{array}{rrcr} \text{in } \ce{CuS}, & \ce{Cu}:\ce{S} &=& 63.5:32 \\ \text{in } \ce{CuO}, & \ce{Cu}:\ce{O} &=& 63.5:16 \\\\ \Rightarrow &\ce{S}: \ce{O} &=& 32:16 \\ & &=&2:1. \end{array}\]

Now in \(\ce{SO2},\) we have

\[\ce{S}:\ce{O} = 32:32= 1:1.\]

Thus the ratio between the two ratios is the following:

\[\frac{2}{1} :\frac{1}{1} = 2:1,\]

which is a simple multiple ratio.