Problem 132 - A Complete Resource Book in Chemistry for JEE Main

Question

In the following questions two statements (Assertion) (A) and Reason (R) are given. Mark (a) If both \(\mathrm{A}\) and \(\mathrm{R}\) are correct and \(\mathrm{R}\) is the correct explanation of \(\mathrm{A}\). (b) If both \(\mathrm{A}\) and \(\mathrm{R}\) are correct but \(\mathrm{R}\) is not the correct expalnation of \(\mathrm{A}\). (c) A is true but \(\mathrm{R}\) is false. (d) A is false but \(R\) is true. (e) \(\mathrm{A}\) and \(\mathrm{R}\) both are false. Assertion: The electron gain enthalpies have large negative values toward the upper right of the periodic table preceding the noble gases. Reason: The effective nuclear charge increases from left to right across a period and consequently it will be easier to add an electron to a smaller atom since the added electron on an average would be closer to the positively charged nucleus.

Step-by-Step Solution

Answer

Answer (a): Both A and R are correct and R is the correct explanation of A.

Step 1: Understanding the Assertion

The assertion states that the electron gain enthalpies (the energy change when an electron is added to a gaseous atom) have large negative values for elements in the upper right part of the periodic table, particularly before the noble gases. This is generally true as elements in this part of the periodic table (like halogens) have a strong tendency to gain electrons to achieve a stable electronic configuration.

Step 2: Understanding the Reason

The reason provided explains that the effective nuclear charge (the net positive charge experienced by an electron in an atom) increases across a period from left to right. This makes the atoms smaller and more positively charged, making it easier for them to attract additional electrons. Hence, adding an electron becomes energetically favorable, especially for atoms smaller in size which allows the added electron to be closer to the nucleus.

Step 3: Evaluating the Truth of the Assertion and Reason

Both the assertion and the reason are accurate. The assertion correctly describes the tendency of elements towards the upper right of the periodic table to have large negative electron gain enthalpies. The reason correctly explains why these elements have such tendencies due to the increasing effective nuclear charge across a period.

Step 4: Assessing if the Reason Explains the Assertion

The reason given explains the assertion well. As the effective nuclear charge increases, the attraction between the nucleus and the added electron increases, making it energetically favorable for atoms to acquire electrons. This is exactly why electron gain enthalpies are more negative moving across a period to the right.

Key Concepts

Electron Gain Enthalpy

Electron Gain Enthalpy refers to the energy change that occurs when an electron is added to a neutral atom in the gas phase. Typically, this process results in the formation of a negative ion. The energy change can be positive or negative, but for most elements, it is negative, indicating that energy is released when the electron is added. This means the process is exothermic as electrons naturally tend to move towards lower energy states.

When considering periodic trends, the elements with the most negative electron gain enthalpies are usually found in the upper right portion of the periodic table, just before the noble gases. This is because these elements, particularly the halogens such as fluorine and chlorine, are only one electron short of achieving a stable, noble gas configuration. The tendency to gain an electron is very strong for these elements, making the enthalpy values particularly negative.

In general, as you move from left to right across a period, the electron gain enthalpies become more negative. This change is linked to the increased effective nuclear charge across a period, which we'll discuss more deeply in the next section.

Effective Nuclear Charge

The Effective Nuclear Charge ( \( Z_{eff} \) ) is a critical concept for understanding the trends within the periodic table. It represents the net positive charge experienced by electrons in an atom. While the nuclear charge increases with the addition of protons in the nucleus as you move across a period, electrons are not subject to the full positive pull of the nucleus due to repulsion from other electrons.

Electrons in the inner shells repel those in the outer shells, reducing the nuclear charge felt by the outer electrons. This electron-electron repulsion is known as shielding or screening effect. The effective nuclear charge is calculated using the formula:

\[ Z_{eff} = Z - S \]
where \( Z \) is the nuclear charge, and \( S \) is the shielding constant.

From left to right across a period, electrons are added to the same energy level while the atomic number increases, resulting in a higher effective nuclear charge. This stronger pull from the nucleus causes the atomic size to decrease, making it easier for the nucleus to attract additional electrons, which results in the large negative electron gain enthalpies seen towards the right of the periodic table.

Periodic Table Trends

Understanding periodic table trends is crucial in chemistry as it helps predict the behavior of elements in various chemical reactions. Among these trends, one of the most noticeable is how atomic size, ionization energy, electronegativity, and electron gain enthalpy change across periods and down groups.

As you go from left to right across a period:

• Atomic size decreases because of the increase in effective nuclear charge, pulling electrons closer to the nucleus.
• Ionization energy increases as more energy is required to remove an electron due to the stronger attraction from the nucleus.
• Electronegativity, or the tendency of an atom to attract electrons, increases for similar reasons.
• Electron gain enthalpy becomes more negative reflecting the greater ease with which an atom can accept an electron.

Moving down a group, these trends show a different pattern:

• Atomic size increases as additional electron shells are added.
• Ionization energy decreases due to the electrons being further from the nucleus.
• Electronegativity decreases as the nucleus's pull on the electrons weakens.
• Electron gain enthalpy becomes less negative or more positive, reflecting the decreased ability to attract additional electrons as the atomic size increases.

These trends demonstrate the interconnected nature of atomic properties and the underlying principles of effective nuclear charge and electron configurations that govern them.