Question

Two elements, \(\mathrm{R}\) and \(\mathrm{Q}\), combine to form two binary compounds. In the first compound, \(14.0 \mathrm{g}\) of \(\mathrm{R}\) combines with \(3.00 \mathrm{g}\) of \(\mathbf{Q .}\) In the second compound, \(7.00 \mathrm{g}\) of \(\mathbf{R}\) combines with \(4.50 \mathrm{g}\) of \(\mathrm{Q}\). Show that these data are in accord with the law of multiple proportions. If the formula of the second compound is \(\mathrm{RQ}\), what is the formula of the first compound?

Short answer

The given data follows the Law of Multiple Proportions as the ratio of masses of Q combined with a fixed mass of R in both compounds is a simple whole number (3:1). Based on this, the formula of the first compound is \( R_3Q \), as there are 3 R atoms combined with a single Q atom.

Step-by-step solution

Understand the law of multiple proportions

The Law of Multiple Proportions states that when two elements combine to form more than one compound, the ratio of the second element that combines with a fixed amount of the first element can be expressed as a simple whole number ratio. Let's find the ratios for the two compounds.

Calculate the ratio of element Q combining with element R in both compounds

In the first compound, we have 14.0g of R combined with 3.00g of Q. In the second compound, we have 7.00g of R combined with 4.50g of Q. For calculating the ratio, let's find the ratio of the masses of Q that combine with a fixed mass of R (say, 1g of R) in each compound. In the first compound, the mass of Q combined with 1g of R will be: \( \frac{3.00}{14.0} = 0.2143g \) In the second compound, the mass of Q combined with 1g of R will be: \( \frac{4.50}{7.00} = 0.6429g \)

Check if the ratio of masses follows the Law of Multiple Proportions

Now, let's find the ratio between the masses of Q that combine with a fixed mass of R in both compounds and check if it is a simple whole number ratio. Ratio of masses of Q: \( \frac{0.6429}{0.2143} = 3.00 \) As the ratio is a simple whole number (3), the given data follows the Law of Multiple Proportions.

Determine the formula of the first compound

The formula of the second compound is given as RQ. Since the ratios of the masses of element Q combined with the same amount of element R in both compounds is 3:1, the amount of Q present in the first compound must be a third of that in the second compound. So, if the second compound has one Q atom (RQ), the first compound must have one third of a Q atom, which is impossible. The smallest whole number ratio is 3:1. Therefore, to obtain the whole number of Q atoms, we need to triple the amount of Q in the first compound to make its ratio to the second compound 3:3 or in simple whole numbers as 1:1. Therefore, the formula of the first compound is \( R_3Q \), as there are 3 R atoms combined with a single Q atom.

Key concepts

Chemical Compounds

Understanding chemical compounds is fundamental to grasping the principles of chemistry. A chemical compound is a substance composed of two or more different elements that are chemically bonded together in a fixed proportion. Each compound has unique properties that are distinct from those of its component elements.

For instance, in our exercise, we encounter two compounds made up of elements R and Q. The uniqueness of these compounds is evident in how the same elements combine in different ratios to yield substances with different compositions. Knowing the weight of each element that goes into a compound, just as we calculated for R and Q, allows us to understand the compound's composition and to predict its properties and behavior during chemical reactions.

Moreover, chemical compounds are represented by chemical formulas that denote the elements and the number of atoms of each element in the compound. For example, RQ and R₃Q are chemical formulas indicating the types and relative amounts of R and Q in each respective compound.

Stoichiometry

Stoichiometry is a section of chemistry that deals with the quantitative relationships between reactants and products in a chemical reaction. When we talk about stoichiometry, we are often referring to the calculation of the masses, volumes, and concentrations of substances involved in a reaction.

In the given exercise, stoichiometry comes into play when we determine the mass ratio of elements R and Q that combine to form different compounds. By fixing the mass of R and comparing how much Q combines with it in each compound, we can utilize stoichiometry to showcase the law of multiple proportions. This application is a perfect example of stoichiometry in action – it is all about ensuring the amounts of reactants combine in the correct proportions as dictated by their molecular composition.

Understanding stoichiometry is not just academic; it is crucial in industries, especially when scaling up chemical reactions from the laboratory to production level, where precision in the composition of chemical substances is paramount for quality and safety.

Chemical Formula Determination

Chemical formula determination is an analytical approach used to identify the elements present in a compound and to ascertain their numbers. It is a key process in chemical sciences that reveals the molecular composition of substances.

To determine the chemical formula, as we've seen in the provided exercise, you would typically analyze the mass of each element in a compound. In the context of the exercise, we're given the masses of elements R and Q in two distinct compounds. By comparing these masses, we're able to deduce a simple whole-number ratio between the elements according to the law of multiple proportions. This simple ratio is the cornerstone of determining the empirical formula, the simplest whole-number ratio of atoms present in a compound.

The empirical formula is a critical piece of information: it tells us the simplest formula with which a compound can be correctly represented. From this, if we know the molecular weight of the substance, we can also work out the molecular formula, which indicates the actual number of atoms in a molecule of the compound. Thus, chemical formula determination is not just about establishing the ratio of elements, but also about providing a solid foundation for understanding the substance's chemical nature and behavior.