Problem 79 - Chemistry Central Science

Question

Hydrogen has two naturally occurring isotopes, \({ }^{1} \mathrm{H}\) and \({ }^{2}\) H. Chlorine also has two naturally occurring isotopes, \({ }^{35} \mathrm{Cl}\) and \({ }^{37} \mathrm{Cl}\). Thus, hydrogen chloride gas consists of four distinct types of molecules: \({ }^{1} \mathrm{H}^{35} \mathrm{Cl},{ }^{1} \mathrm{H}^{37} \mathrm{Cl},{ }^{2} \mathrm{H}^{35} \mathrm{Cl}\), and \({ }^{2} \mathrm{H}^{37} \mathrm{Cl}\). Place these four molecules in order of increasing rate of effusion.

Step-by-Step Solution

Answer

The order of increasing rate of effusion for the four distinct types of hydrogen chloride gas molecules is \({ }^{2} \mathrm{H}^{37} \mathrm{Cl}, { }^{1} \mathrm{H}^{37} \mathrm{Cl}, { }^{2} \mathrm{H}^{35} \mathrm{Cl},\) and \({ }^{1} \mathrm{H}^{35} \mathrm{Cl}\).

Step 1: Calculate the Molar Mass of Each Hydrogen Chloride Gas Molecule

First, find the molar mass of each type of hydrogen chloride molecule by adding the atomic masses of the hydrogen and chlorine isotopes involved. Molar mass of \({ }^{1} \mathrm{H}^{35} \mathrm{Cl} = 1 + 35 = 36\) Molar mass of \({ }^{1} \mathrm{H}^{37} \mathrm{Cl} = 1 + 37 = 38\) Molar mass of \({ }^{2} \mathrm{H}^{35} \mathrm{Cl} = 2 + 35 = 37\) Molar mass of \({ }^{2} \mathrm{H}^{37} \mathrm{Cl} = 2 + 37 = 39\)

Step 2: Apply Graham's Law of Effusion

According to Graham's Law of Effusion, the rate of effusion of a gas is inversely proportional to the square root of its molar mass. Therefore, lower molar mass means higher effusion rate, and higher molar mass means lower effusion rate.

Step 3: Put the Molecules in Order of Increasing Rate of Effusion

Now, just compare the molar mass of each hydrogen chloride gas molecule and arrange them in order of increasing rate of effusion. Remember that a lower molar mass corresponds to a higher effusion rate. The order of increasing rate of effusion is: \({ }^{2} \mathrm{H}^{37} \mathrm{Cl} (39) \rightarrow { }^{1} \mathrm{H}^{37} \mathrm{Cl} (38) \rightarrow { }^{2} \mathrm{H}^{35} \mathrm{Cl} (37) \rightarrow { }^{1} \mathrm{H}^{35} \mathrm{Cl} (36)\)

Key Concepts

Molar Mass

The molar mass of a substance is the mass of one mole of that substance. It's calculated by adding up the atomic masses of the atoms in the molecule. This calculation is crucial, especially when dealing with molecules with isotopes. Isotopes are variants of elements with the same number of protons but different numbers of neutrons, affecting their atomic mass.

For instance, in hydrogen chloride (HCl) molecules, hydrogen has isotopes

• the common hydrogen ( ¹ H)
• deuterium ( ² H)

Chlorine also has isotopes

• chlorine-35 ( ³⁵ Cl)
• chlorine-37 ( ³⁷ Cl).

Calculating the molar mass involves adding these isotopic masses. For example:

• the molar mass of ¹ H ³⁵ Cl is 1 + 35 = 36
• for ¹ H ³⁷ Cl, it is 38

Thus, understanding molar mass is crucial not only for the composition but also for predicting the behavior of gases.

Graham's Law of Effusion

Graham's Law of Effusion provides us with an insight into how gases escape through tiny openings. According to this law, the rate of effusion of a gas is inversely proportional to the square root of its molar mass. In simpler terms, lighter gas molecules effuse faster than heavier ones.

This can be quite useful when determining which type of gas will escape faster in a scenario involving isotopes. For instance, when we know the molar masses of various hydrogen chloride molecules, we can predict their effusion rates. Provided with the formula:\[\text{{Rate of Effusion}} \propto \frac{1}{\sqrt{\text{{Molar Mass}}}}\]we know a molecule with a higher molar mass, like ²H³⁷Cl (39), will effuse slower than a molecule with a lower molar mass, such as ¹H³⁵Cl (36).

This application makes Graham's Law indispensable for chemical processes and scientific experiments involving gas effusion.

Hydrogen Chloride Molecules

Hydrogen chloride molecules are a significant subject of study in chemistry. These molecules are comprised of hydrogen and chlorine atoms, which can vary due to their isotopes. Isotopes are important because they lead to various types of molecules, each with a different mass. Considering isotopes:

• the presence of ¹ H and ² H (deuterium) results in slight mass differences
• while ³⁵ Cl and ³⁷ Cl augment these differences even further .

This creates distinct hydrogen chloride molecules, such as:

• ¹ H ³⁵ Cl
• ¹ H ³⁷ Cl
• ² H ³⁵ Cl
• ² H ³⁷ Cl

The diverse molar masses introduced by these isotopes affect their physical properties, such as how quickly they effuse—a critical aspect explored in Graham’s Law of Effusion. Each unique molecule exhibits characteristics that impact both chemical reactions and practical applications like separation processes in labs.