Hydrogen has two naturally occurring isotopes, 1H and 2H. Chlorine also has two naturally occurring isotopes, 35Cl and 37Cl. Thus, hydrogen chloride gas consists of four distinct types of molecules: 1H35Cl, 1H37Cl, 2H35Cl, and 2H37Cl. Place these four molecules in order of increasing rate of effusion.

Verified step by step guidance

1. Identify the concept of effusion, which is the process by which gas molecules escape through a small hole into a vacuum.
2. Recall Graham's law of effusion, which states that the rate of effusion of a gas is inversely proportional to the square root of its molar mass: \( \text{Rate} \propto \frac{1}{\sqrt{M}} \).
3. Calculate the molar mass of each molecule: \( ^1\text{H}^{35}\text{Cl} \), \( ^1\text{H}^{37}\text{Cl} \), \( ^2\text{H}^{35}\text{Cl} \), and \( ^2\text{H}^{37}\text{Cl} \).
4. Compare the molar masses: the molecule with the smallest molar mass will have the highest rate of effusion, and the one with the largest molar mass will have the lowest rate of effusion.
5. Arrange the molecules in order of increasing molar mass, which will correspond to increasing rate of effusion.

Key Concepts

Effusion

Effusion is the process by which gas molecules escape from a container through a small opening. The rate of effusion is influenced by the mass of the gas molecules; lighter molecules effuse faster than heavier ones. This principle is described by Graham's law, which states that the rate of effusion is inversely proportional to the square root of the molar mass of the gas.

Isotopes

Isotopes are variants of a chemical element that have the same number of protons but different numbers of neutrons, resulting in different atomic masses. For example, hydrogen has isotopes 1H (protium) and 2H (deuterium), while chlorine has 35Cl and 37Cl. The presence of isotopes affects the molar mass of compounds formed, which in turn influences their rates of effusion.

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). In the context of the question, the molar mass of hydrogen chloride molecules varies based on the isotopes of hydrogen and chlorine present. The different combinations of isotopes lead to distinct molar masses, which are crucial for determining the order of effusion rates among the four types of hydrogen chloride molecules.