Chlorine has two natural isotopes: \(_{17}^{37} \mathrm{Cl}\) and 35 17 \(\mathrm{Cl}\) Hydrogen reacts with chlorine to form the compound 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

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In the reaction between hydrogen and the two natural isotopes of chlorine (\(_{17}^{35}\mathrm{Cl}\) and \(_{17}^{37}\mathrm{Cl}\)) to form HCl, a given amount of hydrogen reacts with different masses of the two chlorine isotopes: - For \(_{17}^{35}\mathrm{Cl}\): one mole of hydrogen reacts with 35 grams of chlorine - For \(_{17}^{37}\mathrm{Cl}\): one mole of hydrogen reacts with 37 grams of chlorine However, this does not conflict with the law of definite proportion, as the mass ratio of hydrogen and either chlorine isotope in HCl remains constant. The law states that a chemical compound always contains its component elements in a fixed mass ratio regardless of its source, and since the isotopes have the same chemical behavior, their reactions with hydrogen produce HCl with the same stoichiometry.

Step by step solution

01

Determine the balanced chemical equation for the reaction

The balanced chemical equation represents the reaction between hydrogen and chlorine. We know that hydrogen is in group 1 of the periodic table and forms a monovalent bond with other elements. The same goes for chlorine. Thus, the balanced chemical equation for the reaction can be written as: \[ \mathrm{H_2 + Cl_2 \rightarrow 2HCl} \]
02

Interpret the balanced chemical equation for both isotopes of chlorine

The balanced equation tells us that one molecule of dihydrogen (\( \mathrm{H_2} \)) reacts with one molecule of dichlorine (\( \mathrm{Cl_2} \)), either \( _{17}^{35} \mathrm{Cl} \) or \( _{17}^{37} \mathrm{Cl}\), to form two molecules of hydrogen chloride (\(\mathrm{HCl}\)). Since both isotopes of chlorine have the same chemical behavior, they will react similarly with hydrogen to form HCl.
03

Examine the masses of the two chlorine isotopes in the reaction

The atomic mass of the two isotopes of chlorine differs. The mass of \( _{17}^{35} \mathrm{Cl} \) is 35 daltons, while the mass of \( _{17}^{37} \mathrm{Cl} \) is 37 daltons. Therefore, it is essential to take this mass difference into account when comparing the masses of chlorine reacting with hydrogen. Let's consider one mole of each chlorine isotope reacting with one mole of hydrogen: - For \(_{17}^{35}\mathrm{Cl}\): one mole of hydrogen reacts with 35 grams of chlorine - For \(_{17}^{37}\mathrm{Cl}\): one mole of hydrogen reacts with 37 grams of chlorine
04

Evaluate whether this conflicts with the law of definite proportion

The law of definite proportions states that a chemical compound always contains its component elements in a fixed mass ratio regardless of its source. In the case of HCl, it will always have a constant mass ratio between hydrogen and chlorine, made of either \(_{17}^{35}\mathrm{Cl}\) or \(_{17}^{37}\mathrm{Cl}\), no matter what source it comes from. Since both isotopes of chlorine have the same chemical behavior, they will react similarly with hydrogen and form HCl with the same stoichiometry. Therefore, the law of definite proportions does not conflict in this case, as the mass ratio of the elements in HCl remains constant.

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