Question

Chlorine has two natural isotopes: \({ }_{1}^{\mathrm{j}} \mathrm{Cl}\) and \({ }_{1}{ }^{35} \mathrm{Cl} .\) Hydrogen reacts with chlorine to form the compound \(\mathrm{HCl}\). Would a given amount of hydrogen react with different masses of the two chlorine isotopes? Does this conflict with the law of definite proportion? Why or why not?

Short answer

A given amount of hydrogen will react with different masses of the two chlorine isotopes to form HCl, but this does not conflict with the law of definite proportions. The law states that a chemical compound always has the same proportion of elements by mass, and the ratio of hydrogen to chlorine in both versions of HCl is 1:1, maintaining a fixed proportion of reactants and products. Although the isotopes have different masses, their chemical properties are the same, so the reaction between hydrogen and each chlorine isotope is still one-to-one.

Step-by-step solution

Understand the law of definite proportions

The law of definite proportions, also known as the law of constant composition, states that a chemical compound always has the same proportion of elements by mass, regardless of its origin or method of preparation. In other words, the masses of the elements in a compound are found in fixed ratios.

Examine the two isotopes of chlorine

Chlorine has two natural isotopes: \({ }_{1}^{\mathrm{35}} \mathrm{Cl}\) and \({ }_{1}{ }^{37} \mathrm{Cl}\). While they have the same atomic number (17) and chemical properties, they have different mass numbers due to the number of neutrons in their nucleus. - For \({ }_{1}^{\mathrm{35}} \mathrm{Cl}\), the mass number is 35, meaning it has 18 neutrons. - For \({ }_{1}^{\mathrm{37}} \mathrm{Cl}\), the mass number is 37, meaning it has 20 neutrons. These differences in neutron number result in different atomic masses.

Analyze Hydrogen reacting with both chlorine isotopes

Let's examine how hydrogen reacts with the two chlorine isotopes to form HCl: \[\begin{aligned} \ce{H + \( { }_{1}^{\mathrm{35}} \mathrm{Cl} \) &-> H^{35}Cl} \\ \ce{H + \( { }_{1}^{\mathrm{37}} \mathrm{Cl} \) &-> H^{37}Cl} \end{aligned}\] Keep in mind that both isotopes of chlorine have the same chemical properties, and hydrogen will react with one atom of chlorine to form one molecule of HCl in either case. Thus, the chemical reaction between hydrogen and each chlorine isotope is still one-to-one.

Mass ratio of reactants

When a given amount of hydrogen reacts with an equal amount of chlorine, the mass ratio of reactants, H:Cl, remains fixed for \(H^{35}Cl\) and \(H^{37}Cl\), as hydrogen reacts with one atom of each isotope, forming one molecule of HCl.

Determine if there's a conflict with the law of definite proportions

Since the chemical reaction between hydrogen and both chlorine isotopes results in a fixed proportion of reactants and products, there is no conflict with the law of definite proportions. The masses of the elements in HCl resulting from reactions with the two different isotopes are still in a fixed ratio, because hydrogen reacts with one atom of each chlorine isotope, forming one molecule of HCl. Additionally, even though the isotopes have different masses, their chemical properties remain the same, and the ratio of hydrogen to chlorine in both versions of HCl is 1:1.

Key concepts

Chemical Isotopes

Chemical isotopes are variants of the same chemical element that have identical numbers of protons but different numbers of neutrons within their nuclei, leading to different mass numbers. Despite these differences, isotopes of an element have the same position in the periodic table and very similar chemical behaviors.

For example, chlorine has two common isotopes, often referred to by their mass numbers as chlorine-35 and chlorine-37. The presence of isotopes illustrates the nuance in the law of definite proportions: although the proportion of elements in a chemical compound is consistent, the mass of a specific element may vary slightly due to different isotopes being involved in reactions. This does not conflict with the law, as the resulting compounds still maintain constant proportion by element, not by isotope. The chemical properties, including reactivity, are not significantly altered by the presence of isotopes, allowing a substance like HCl to form consistently regardless of the isotope of chlorine involved.

Chemical Composition

Chemical composition is a description of the types and proportions of elements that constitute a chemical compound. It is fundamental to the law of definite proportions, which asserts that a chemical compound always contains exactly the same proportion of elements by mass. This law reveals that the composition is precise and predictable, allowing us to deduce the formula and structure of a compound based on its constituent elements.

For instance, whether chlorine-35 or chlorine-37 is involved in the formation of hydrogen chloride (HCl), the chemical composition of HCl remains consistent: each molecule contains one hydrogen atom and one chlorine atom. The slight mass difference between the isotopes does not affect the stoichiometry of the reaction, only the mass of the individual molecules. This is a cornerstone of chemical understanding, ensuring that the substances can be accurately described and used in further chemical processes or applications.

Stoichiometry

Stoichiometry is the quantitative relationship between reactants and products in a chemical reaction. It's derived from the Greek words 'stoicheion' (element) and 'metron' (measure), and it is crucial for predicting the amounts of substances consumed and produced in a reaction.

Understanding Stoichiometry in Reactions

In the context of specifying amounts, stoichiometry takes the law of definite proportions and applies it to the reactions. Let's take the formation of HCl as an example. Whether hydrogen reacts with chlorine-35 or chlorine-37, the stoichiometry of the reaction dictates that one hydrogen atom will react with one chlorine atom to form one molecule of HCl. This is expressed by the balanced equation:\[ \text{H} + \text{Cl} \rightarrow \text{HCl} \]The stoichiometric coefficients in a balanced chemical equation indicate the ratio of reactants to products. In their simpliest form, they are 1:1 for this reaction, showing that a fixed, definite ratio is maintained, in accordance with the law of definite proportions.