A transition metal 'M' among Sc, Ti, V , Cr, Mn and Fe has the highest second ionisation enthalpy. The spin only magnetic moment value of M+
ion is ______ BM (Near integer) (Given atomic number Sc : 21, Ti : 22, V : 23, Cr : 24, Mn : 25, Fe : 26)
ion is ______ BM (Near integer) (Given atomic number Sc : 21, Ti : 22, V : 23, Cr : 24, Mn : 25, Fe : 26)
Correct Answer: 6
Approach Solution - 1
The electronic configuration of Cr is [Ar] 3d5 4s1. Upon losing one electron, Cr becomes Cr+ with the configuration [Ar] 3d5. The presence of a half-filled d subshell in Cr+ offers additional stability, contributing to a higher second ionisation enthalpy.
Now, the spin-only magnetic moment for a d5 configuration is calculated using the formula:
µ = √n(n + 2) BM
Where n is the number of unpaired electrons. For Cr+, n = 5. Thus,
µ = √5(5 + 2) = √35 ≈ 5.92 BM.
Since the question asks for the value as a near integer, we round this to 6 BM.
Therefore, the spin-only magnetic moment of the M+ ion is 6 BM, which lies within the expected range of 6,6.
Approach Solution -2
To determine which transition metal 'M' has the highest second ionization enthalpy among Sc, Ti, V, Cr, Mn, and Fe, we need to analyze the electronic configurations and related properties. The second ionization enthalpy is the energy required to remove an electron from a singly charged cation (M+). It is typically high for elements where removing an electron significantly disrupts a stable configuration.
1. Determine the electronic configuration of each element:
- Sc (Z=21): [Ar] 3d1 4s2
- Ti (Z=22): [Ar] 3d2 4s2
- V (Z=23): [Ar] 3d3 4s2
- Cr (Z=24): [Ar] 3d5 4s1
- Mn (Z=25): [Ar] 3d5 4s2
- Fe (Z=26): [Ar] 3d6 4s2
2. Evaluate the second ionization: Removing the second electron from M+.
3. Cr ([Ar] 3d5) has a half-filled 3d subshell, which is notably stable. Removing one more electron to form Cr2+ disrupts this stability, resulting in high ionization enthalpy.
Answer: Cr has the highest second ionization enthalpy.
4. Find the spin-only magnetic moment of Cr+ (d5 configuration):
The magnetic moment (µ) is given by µ=√n(n+2), where n is the number of unpaired electrons.
- Cr+ has 5 unpaired electrons: 3d5
- µ=√5(5+2)=√35 ≈ 5.92 BM
5. Verification:
The calculated magnetic moment is approximately 6 BM, which is within the given range of 6,6.
Conclusively, the spin-only magnetic moment of Cr+ ion is approximately 6 BM.
Top Questions on Enthalpy change
- The group 14 elements A and B have the first ionisation enthalpy values of 708 and 715 kJ mol$^{-1}$ respectively. The above values are lowest among their group members. The nature of their ions A$^{2+}$ and B$^{4+}$ respectively is:
- JEE Main - 2025
- Chemistry
- Enthalpy change
- The incorrect relationship in the following pairs in relation to ionisation enthalpies is:
- JEE Main - 2025
- Chemistry
- Enthalpy change
- Given below are two statements:
Statement (I): The radius of isoelectronic species increases in the order: \[ \text{Mg}^{2+} < \text{Na}^{+} < \text{F}^{-} < \text{O}^{2-} \] Statement (II): The magnitude of electron gain enthalpy of halogens decreases in the order: \[ \text{Cl} > \text{F} > \text{Br} > \text{I} \] In light of the above statements, choose the most appropriate answer from the options given below:- JEE Main - 2025
- Chemistry
- Enthalpy change
- Consider the following cases of standard enthalpy of reaction (\( \Delta H_f^\circ \) in kJ mol\(^{-1}\)): \[ \text{C}_2\text{H}_6(g) + 7 \text{O}_2(g) \rightarrow 2 \text{CO}_2(g) + 3 \text{H}_2\text{O}(l) \quad \Delta H_1^\circ = -1550 \] \[ \text{C(graphite)} + \text{O}_2(g) \rightarrow \text{CO}_2(g) \quad \Delta H_2^\circ = -393.5 \] \[ \text{H}_2(g) + \frac{1}{2} \text{O}_2(g) \rightarrow \text{H}_2\text{O}(g) \quad \Delta H_3^\circ = -286 \] The magnitude of \( \Delta H_f^\circ \) of \( \text{C}_2\text{H}_6(g) \) is \(\_\_\_\_\_\) kJ mol\(^{-1}\) (Nearest integer).
- JEE Main - 2025
- Chemistry
- Enthalpy change
- The bond dissociation energies of gaseous H2, Cl2, and HCl are 104, 58, and 103 kcal, respectively. The enthalpy of formation of HCl gas would be:
- BCECE - 2025
- Chemistry
- Enthalpy change
Questions Asked in JEE Main exam
- A thin convex lens of focal length \( 5 \) cm and a thin concave lens of focal length \( 4 \) cm are combined together (without any gap), and this combination has magnification \( m_1 \) when an object is placed \( 10 \) cm before the convex lens.
Keeping the positions of the convex lens and the object undisturbed, a gap of \( 1 \) cm is introduced between the lenses by moving the concave lens away. This leads to a change in magnification of the total lens system to \( m_2 \).
The value of \( \dfrac{m_1}{m_2} \) is
- The escape velocity from a spherical planet \(A\) is \(10\ \text{km/s}\). The escape velocity from another planet \(B\), whose density and radius are \(10%\) of those of planet \(A\), is _______ m/s.
- JEE Main - 2026
- Gravitation
\(XPQY\) is a vertical smooth long loop having a total resistance \(R\), where \(PX\) is parallel to \(QY\) and the separation between them is \(l\). A constant magnetic field \(B\) perpendicular to the plane of the loop exists in the entire space. A rod \(CD\) of length \(L\,(L>l)\) and mass \(m\) is made to slide down from rest under gravity as shown. The terminal speed acquired by the rod is _______ m/s.
- JEE Main - 2026
- Ray optics and optical instruments
Net gravitational force at the center of a square is found to be \( F_1 \) when four particles having masses \( M, 2M, 3M \) and \( 4M \) are placed at the four corners of the square as shown in figure, and it is \( F_2 \) when the positions of \( 3M \) and \( 4M \) are interchanged. The ratio \( \dfrac{F_1}{F_2} = \dfrac{\alpha}{\sqrt{5}} \). The value of \( \alpha \) is
- JEE Main - 2026
- Gravitation
A meter bridge with two resistances \( R_1 \) and \( R_2 \) as shown in figure was balanced (null point) at 40 cm from the point \( P \). The null point changed to 50 cm from the point \( P \), when a \( 16\,\Omega \) resistance is connected in parallel to \( R_2 \). The values of resistances \( R_1 \) and \( R_2 \) are
- JEE Main - 2026
- Meter Bridge