Question

Chlorine has two natural isotopes: \({ }_{1} 7 \mathrm{Cl}\) and \(\left.{ }_{1}^{3}\right\\} \mathrm{Cl}\). 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 reacts with different masses of the two chlorine isotopes, resulting in slightly different mass ratios for hydrogen-to-chlorine in the HCl compounds formed by each isotope, \(0.0286\) for \(HCl^{35}\) and \(0.0270\) for \(HCl^{37}\). However, this does not conflict with the law of definite proportion, as the proportion of hydrogen-to-chlorine by mass remains consistent within a sample of HCl formed with the same isotopic chlorine.

Step-by-step solution

The atomic masses of the two natural isotopes of chlorine are: 1. For \(Cl^{35}\) (17 protons + 18 neutrons): \(17 + 18 = 35\) 2. For \(^{37}Cl\) (17 protons + 20 neutrons): \(17 + 20 = 37\) #step2# Calculate the mass ratios of hydrogen-to-chlorine in each HCl formed by the different isotopes

To calculate the mass ratios for the two reactions, we will divide the atomic mass of hydrogen (1 amu) by the atomic mass of each chlorine isotope: 1. For HCl formed by hydrogen and \(Cl^{35}\): \(\frac{1}{35} \approx 0.0286\) 2. For HCl formed by hydrogen and \(^{37}Cl\): \(\frac{1}{37} \approx 0.0270\) #step3# Compare the two mass ratios to the law of definite proportion

We have the following mass ratios for hydrogen-to-chlorine in the HCl compound formed by each isotope: 1. \(0.0286\) for \(HCl^{35}\) 2. \(0.0270\) for \(HCl^{37}\) The mass ratios are slightly different for each compound formed with different chlorine isotopes. However, this does not conflict with the law of definite proportion. The law of definite proportion holds true if we consider each isotopic form of the compound separately. Thus, the proportion of hydrogen-to-chlorine by mass in a sample of HCl made up of the same isotopic chlorine will be consistent. #step4# Conclusion

A given amount of hydrogen reacts with different masses of the two chlorine isotopes to form HCl. However, this does not conflict with the law of definite proportion, as the proportion of hydrogen-to-chlorine by mass remains consistent within a sample of HCl formed with the same isotopic chlorine.

Key concepts

Chemical Isotopes

Chemical isotopes are variants of a particular chemical element that share the same number of protons but differ in the number of neutrons. This variation in neutron count results in differences in atomic mass. For instance, chlorine has two primary natural isotopes: Cl³⁵ and Cl³⁷. Despite having different atomic masses, these isotopes of chlorine still behave similarly in chemical reactions, such as combining with hydrogen to form hydrochloric acid (HCl).

When exploring how isotopes react with other elements, it's crucial to acknowledge that the fundamental chemical behavior is unaffected. This means that regardless of whether Cl³⁵ or Cl³⁷ reacts with hydrogen, the resulting compound is hydrochloric acid. However, the mass of the compound will slightly differ, corresponding to the isotope of chlorine involved in the reaction.

Hydrogen and Chlorine Reaction

The reaction between hydrogen and chlorine to form hydrochloric acid is a classic example of a chemical synthesis reaction. Individually, hydrogen (H) is a diatomic gas, and chlorine (Cl) is a diatomic, toxic gas that exhibits a greenish color. When they react, the products differ significantly from the reactants both physically and chemically.

Regarding the law of definite proportions, hydrogen always combines with chlorine in a 1:1 molar ratio to form HCl, which is also a gas but with distinct properties used in various applications, including the production of chlorine-containing compounds. This simple stoichiometry means that no matter what isotope of chlorine is participating in the reaction, the ratio of the atoms remains one hydrogen atom to one chlorine atom, underscoring the law's validity even when isotopes are involved.

Atomic Mass

Atomic mass is a fundamental concept in chemistry, which refers to the mass of an atom, typically measured in atomic mass units (amu). Each element's atomic mass listed on the periodic table is the weighted average of all its isotopes occurring in nature, considering both the mass and abundance of each isotope.

In the case of chlorine, the atomic mass is approximately 35.5 amu, which accounts for the natural abundance of the isotopes Cl³⁵ and Cl³⁷. When we talk about isotopic atomic masses, Cl³⁵ has an atomic mass of 35 amu (17 protons plus 18 neutrons) and Cl³⁷ has 37 amu (17 protons plus 20 neutrons). This difference in mass is crucial when considering the mass ratio of hydrogen to chlorine in compounds like HCl, as the isotopic composition will influence the mass but not the chemical stoichiometry of the compound.