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Q3.25:
Would you expect the first ionization enthalpies for two isotopes of the same element to be the same or different? Justify your answer.
Solution :
Theoretical Foundation: Ionization Enthalpy
The first ionization enthalpy ($\Delta_i H_1$) is defined as the minimum amount of energy required to remove the most loosely bound electron from an isolated gaseous atom in its ground state. The energy required for this process is primarily governed by the effective nuclear charge ($Z_{eff}$) and the principal quantum number ($n$) of the valence shell [Per Coulomb’s Law: $F = k \cdot \frac{q_1 q_2}{r^2}$].
Step 1: Characterizing Isotopes
Isotopes are atoms of the same element that possess the same atomic number ($Z$, number of protons) but a different mass number ($A$, number of neutrons). Consequently, isotopes of a given element:
- Possess identical electronic configurations ($ns^x np^y ...$).
- Possess the same number of protons and electrons.
- Exhibit identical $Z_{eff}$ acting on the valence electrons.
Step 2: Analyzing the Impact of Mass on Electronic Interactions
While isotopes differ in nuclear mass due to the number of neutrons, neutrons do not participate in the electromagnetic interactions that bind electrons to the nucleus. The potential energy ($V$) of the valence electron is given by:
$V = -\frac{Ze^2}{4\pi\epsilon_0 r}$
Since $Z$ (the atomic number) is constant for two isotopes, the electrostatic potential energy remains invariant. Thus, the work required to overcome this potential to remove an electron is mathematically identical for isotopes [Based on the Postulates of Quantum Mechanics].
Step 3: Comparative Analysis
The following table delineates the properties of isotopes concerning ionization energetics:
| Property | Isotope A | Isotope B |
|---|---|---|
| Proton Count ($p^+$) | $Z$ | $Z$ |
| Electron Count ($e^-$) | $Z$ | $Z$ |
| Electronic Configuration | Identical | Identical |
| Ionization Enthalpy ($\Delta_i H_1$) | $\Delta_i H_1$ | $\Delta_i H_1$ |
Visual Representation of Isotopic Electron Shells
Logical Deduction
Since the first ionization enthalpy is independent of the nuclear mass (as neutrons do not affect the electronic environment or the nuclear charge), the energy required to remove the electron remains constant. While there may be negligible quantum mechanical differences (related to the reduced mass of the electron-nucleus system), these are far below the scale of standard chemical thermodynamic measurements.
Final Solution: The first ionization enthalpies for two isotopes of the same element are expected to be the same because isotopes have identical electronic configurations and effective nuclear charges, which are the primary determinants of ionization energy.
More Questions from Class 11 Chemistry Classification of Elements and Periodicity in Properties EXERCISES
- Q3.1: What is the basic theme of organisation in the periodic table?
- Q3.1: What is the basic theme of organisation in the periodic table?
- Q3.10: How do atomic radius vary in a period and in a group? How do you explain the variation?
- Q3.10: How do atomic radius vary in a period and in a group? How do you explain the variation?
- Q3.11(i): What do you understand by isoelectronic species? Name a species that will be isoelectronic with each of the following atoms or ions. (i) $F^{-}$
- Q3.11(i): What do you understand by isoelectronic species? Name a species that will be isoelectronic with each of the following atoms or ions. (i) (F^{-})
- Q3.11(ii): What do you understand by isoelectronic species? Name a species that will be isoelectronic with each of the following atoms or ions. (ii) $Ar$
- Q3.11(ii): What do you understand by isoelectronic species? Name a species that will be isoelectronic with each of the following atoms or ions. (ii) Ar
- Q3.11(iii): What do you understand by isoelectronic species? Name a species that will be isoelectronic with each of the following atoms or ions. (iii) $Mg^{2+}$
- Q3.11(iii): What do you understand by isoelectronic species? Name a species that will be isoelectronic with each of the following atoms or ions. (iii) (Mg^{2+})
- Q3.11(iv): What do you understand by isoelectronic species? Name a species that will be isoelectronic with each of the following atoms or ions. (iv) $Rb^{+}$
- Q3.11(iv): What do you understand by isoelectronic species? Name a species that will be isoelectronic with each of the following atoms or ions. (iv) (Rb^{+})
- Q3.12(a): Consider the following species : $N^{3-}$, $O^{2-}$, $F^{-}$, $Na^{+}$, $Mg^{2+}$ and $Al^{3+}$ (a) What is common in them?
- Q3.12(a): Consider the following species: (N^{3-}), (O^{2-}), (F^{-}), (Na^{+}), (Mg^{2+}) and (Al^{3+}) (a) What is common in them?
- Q3.12(b): Consider the following species : $N^{3-}$, $O^{2-}$, $F^{-}$, $Na^{+}$, $Mg^{2+}$ and $Al^{3+}$ (b) Arrange them in the order of increasing ionic radii.
- Q3.12(b): Consider the following species: (N^{3-}), (O^{2-}), (F^{-}), (Na^{+}), (Mg^{2+}) and (Al^{3+}) (b) Arrange them in the order of increasing ionic radii.
- Q3.13: Explain why cation are smaller and anions larger in radii than their parent atoms?
- Q3.13: Explain why cation are smaller and anions larger in radii than their parent atoms?
- Q3.14: What is the significance of the terms — ‘isolated gaseous atom’ and ‘ground state’ while defining the ionization enthalpy and electron gain enthalpy?
- Q3.14: What is the significance of the terms — ‘isolated gaseous atom’ and ‘ground state’ while defining the ionization enthalpy and electron gain enthalpy? Hint : Requirements for comparison purposes.
- Q3.15: Energy of an electron in the ground state of the hydrogen atom is $-2.18 imes 10^{-18}J$. Calculate the ionization enthalpy of atomic hydrogen in terms of $J mol^{-1}$.
- Q3.15: Energy of an electron in the ground state of the hydrogen atom is (–2.18 \times 10^{-18}J). Calculate the ionization enthalpy of atomic hydrogen in terms of (J mol^{-1}). Hint: Apply the idea of mole concept to derive the answer.
- Q3.16(i): Among the second period elements the actual ionization enthalpies are in the order $Li < B < Be < C < O < N < F < Ne$. Explain why (i) $Be$ has higher $\Delta_{i} H$ than $B$
- Q3.16(i): Among the second period elements the actual ionization enthalpies are in the order (Li < B < Be < C < O < N < F < Ne). Explain why (i) Be has higher (\Delta_{i}H) than B
- Q3.16(ii): Among the second period elements the actual ionization enthalpies are in the order $Li < B < Be < C < O < N < F < Ne$. Explain why (ii) $O$ has lower $\Delta_{i} H$ than $N$ and $F$?
- Q3.16(ii): Among the second period elements the actual ionization enthalpies are in the order (Li < B < Be < C < O < N < F < Ne). Explain why (ii) O has lower (\Delta_{i}H) than N and F?
- Q3.17: How would you explain the fact that the first ionization enthalpy of sodium is lower than that of magnesium but its second ionization enthalpy is higher than that of magnesium?
- Q3.17: How would you explain the fact that the first ionization enthalpy of sodium is lower than that of magnesium but its second ionization enthalpy is higher than that of magnesium?
- Q3.18: What are the various factors due to which the ionization enthalpy of the main group elements tends to decrease down a group?
- Q3.18: What are the various factors due to which the ionization enthalpy of the main group elements tends to decrease down a group?
- Q3.19: The first ionization enthalpy values (in $kJ mol^{-1}$) of group 13 elements are : B Al Ga In Tl 801 577 579 558 589 How would you explain this deviation from the general trend ?
- Q3.19: The first ionization enthalpy values (in (kJ mol^{-1})) of group 13 elements are : B 801, Al 577, Ga 579, In 558, Tl 589 How would you explain this deviation from the general trend ?
- Q3.2: Which important property did Mendeleev use to classify the elements in his periodic table and did he stick to that?
- Q3.2: Which important property did Mendeleev use to classify the elements in his periodic table and did he stick to that?
- Q3.20(i): Which of the following pairs of elements would have a more negative electron gain enthalpy? (i) $O$ or $F$
- Q3.20(i): Which of the following pairs of elements would have a more negative electron gain enthalpy? (i) O or F
- Q3.20(ii): Which of the following pairs of elements would have a more negative electron gain enthalpy? (ii) $F$ or $Cl$
- Q3.20(ii): Which of the following pairs of elements would have a more negative electron gain enthalpy? (ii) F or Cl
- Q3.21: Would you expect the second electron gain enthalpy of $O$ as positive, more negative or less negative than the first? Justify your answer.
- Q3.21: Would you expect the second electron gain enthalpy of O as positive, more negative or less negative than the first? Justify your answer.
- Q3.22: What is the basic difference between the terms electron gain enthalpy and electronegativity?
- Q3.22: What is the basic difference between the terms electron gain enthalpy and electronegativity?
- Q3.23: How would you react to the statement that the electronegativity of $N$ on Pauling scale is 3.0 in all the nitrogen compounds?
- Q3.23: How would you react to the statement that the electronegativity of N on Pauling scale is 3.0 in all the nitrogen compounds?
- Q3.24(a): Describe the theory associated with the radius of an atom as it (a) gains an electron
- Q3.24(a): Describe the theory associated with the radius of an atom as it (a) gains an electron
- Q3.24(b): Describe the theory associated with the radius of an atom as it (b) loses an electron
- Q3.24(b): Describe the theory associated with the radius of an atom as it (b) loses an electron
- Q3.25: Would you expect the first ionization enthalpies for two isotopes of the same element to be the same or different? Justify your answer.
- Q3.26: What are the major differences between metals and non-metals?
- Q3.26: What are the major differences between metals and non-metals?
- Q3.27(a): Use the periodic table to answer the following questions. (a) Identify an element with five electrons in the outer subshell.
- Q3.27(a): Use the periodic table to answer the following questions. (a) Identify an element with five electrons in the outer subshell.
- Q3.27(b): Use the periodic table to answer the following questions. (b) Identify an element that would tend to lose two electrons.
- Q3.27(b): Use the periodic table to answer the following questions. (b) Identify an element that would tend to lose two electrons.
- Q3.27(c): Use the periodic table to answer the following questions. (c) Identify an element that would tend to gain two electrons.
- Q3.27(c): Use the periodic table to answer the following questions. (c) Identify an element that would tend to gain two electrons.
- Q3.27(d): Use the periodic table to answer the following questions. (d) Identify the group having metal, non-metal, liquid as well as gas at the room temperature.
- Q3.27(d): Use the periodic table to answer the following questions. (d) Identify the group having metal, non-metal, liquid as well as gas at the room temperature.
- Q3.28: The increasing order of reactivity among group 1 elements is $Li < Na < K < Rb < Cs$ whereas that among group 17 elements is $F > Cl > Br > I$. Explain.
- Q3.28: The increasing order of reactivity among group 1 elements is (Li < Na < K < Rb < Cs) whereas that among group 17 elements is (F > CI > Br > I). Explain.
- Q3.29: Write the general outer electronic configuration of $s$-, $p$-, $d$- and $f$- block elements.
- Q3.29: Write the general outer electronic configuration of s-, p-, d- and f- block elements.
- Q3.3: What is the basic difference in approach between the Mendeleev’s Periodic Law and the Modern Periodic Law?
- Q3.3: What is the basic difference in approach between the Mendeleev’s Periodic Law and the Modern Periodic Law?
- Q3.30(i): Assign the position of the element having outer electronic configuration (i) $ns^{2}np^{4}$ for $n=3$
- Q3.30(i): Assign the position of the element having outer electronic configuration (i) (ns^{2}np^{4}) for (n=3)
- Q3.30(ii): Assign the position of the element having outer electronic configuration (ii) $(n-1)d^{2}ns^{2}$ for $n=4$, and
- Q3.30(ii): Assign the position of the element having outer electronic configuration (ii) ((n-1)d^{2}ns^{2}) for (n=4)
- Q3.30(iii): Assign the position of the element having outer electronic configuration (iii) $(n-2) f^{7} (n-1)d^{1}ns^{2}$ for $n=6$, in the periodic table.
- Q3.30(iii): Assign the position of the element having outer electronic configuration (iii) ((n-2)f^{7}(n-1)d^{1}ns^{2}) for (n=6), in the periodic table.
- Q3.31(a): The first ($\Delta_{i}H_{1}$) and the second ($\Delta_{i}H_{2}$) ionization enthalpies (in kJ $mol^{-1}$) and the ($\Delta_{eg}H$) electron gain enthalpy (in kJ $mol^{-1}$) of a few elements are given below: Elements $\Delta H_{1}$ $\Delta H_{2}$ $\Delta_{eg}H$ I 520 7300 –60 II 419 3051 –48 III 1681 3374 –328 IV 1008 1846 –295 V 2372 5251 +48 VI 738 1451 –40 Which of the above elements is likely to be : (a) the least reactive element.
- Q3.31(a): The first ((\Delta_{i}H_{1})) and the second ((\Delta_{i}H_{2})) ionization enthalpies (in (kJ mol^{-1})) and the ((\Delta_{eg}H)) electron gain enthalpy (in (kJ mol^{-1})) of a few elements are given below: Which of the above elements is likely to be : (a) the least reactive element.
- Q3.31(b): The first ($\Delta_{i}H_{1}$) and the second ($\Delta_{i}H_{2}$) ionization enthalpies (in kJ $mol^{-1}$) and the ($\Delta_{eg}H$) electron gain enthalpy (in kJ $mol^{-1}$) of a few elements are given below: Elements $\Delta H_{1}$ $\Delta H_{2}$ $\Delta_{eg}H$ I 520 7300 –60 II 419 3051 –48 III 1681 3374 –328 IV 1008 1846 –295 V 2372 5251 +48 VI 738 1451 –40 Which of the above elements is likely to be : (b) the most reactive metal.
- Q3.31(b): The first ((\Delta_{i}H_{1})) and the second ((\Delta_{i}H_{2})) ionization enthalpies (in (kJ mol^{-1})) and the ((\Delta_{eg}H)) electron gain enthalpy (in (kJ mol^{-1})) of a few elements are given below: (b) the most reactive metal.
- Q3.31(c): The first ($\Delta_{i}H_{1}$) and the second ($\Delta_{i}H_{2}$) ionization enthalpies (in kJ $mol^{-1}$) and the ($\Delta_{eg}H$) electron gain enthalpy (in kJ $mol^{-1}$) of a few elements are given below: Elements $\Delta H_{1}$ $\Delta H_{2}$ $\Delta_{eg}H$ I 520 7300 –60 II 419 3051 –48 III 1681 3374 –328 IV 1008 1846 –295 V 2372 5251 +48 VI 738 1451 –40 Which of the above elements is likely to be : (c) the most reactive non-metal.
- Q3.31(c): The first ((\Delta_{i}H_{1})) and the second ((\Delta_{i}H_{2})) ionization enthalpies (in (kJ mol^{-1})) and the ((\Delta_{eg}H)) electron gain enthalpy (in (kJ mol^{-1})) of a few elements are given below: (c) the most reactive non-metal.
- Q3.31(d): The first ($\Delta_{i}H_{1}$) and the second ($\Delta_{i}H_{2}$) ionization enthalpies (in kJ $mol^{-1}$) and the ($\Delta_{eg}H$) electron gain enthalpy (in kJ $mol^{-1}$) of a few elements are given below: Elements $\Delta H_{1}$ $\Delta H_{2}$ $\Delta_{eg}H$ I 520 7300 –60 II 419 3051 –48 III 1681 3374 –328 IV 1008 1846 –295 V 2372 5251 +48 VI 738 1451 –40 Which of the above elements is likely to be : (d) the least reactive non-metal.
- Q3.31(d): The first ((\Delta_{i}H_{1})) and the second ((\Delta_{i}H_{2})) ionization enthalpies (in (kJ mol^{-1})) and the ((\Delta_{eg}H)) electron gain enthalpy (in (kJ mol^{-1})) of a few elements are given below: (d) the least reactive non-metal.
- Q3.31(e): The first ($\Delta_{i}H_{1}$) and the second ($\Delta_{i}H_{2}$) ionization enthalpies (in kJ $mol^{-1}$) and the ($\Delta_{eg}H$) electron gain enthalpy (in kJ $mol^{-1}$) of a few elements are given below: Elements $\Delta H_{1}$ $\Delta H_{2}$ $\Delta_{eg}H$ I 520 7300 –60 II 419 3051 –48 III 1681 3374 –328 IV 1008 1846 –295 V 2372 5251 +48 VI 738 1451 –40 Which of the above elements is likely to be : (e) the metal which can form a stable binary halide of the formula $MX_{2}$($X$=halogen).
- Q3.31(e): The first ((\Delta_{i}H_{1})) and the second ((\Delta_{i}H_{2})) ionization enthalpies (in (kJ mol^{-1})) and the ((\Delta_{eg}H)) electron gain enthalpy (in (kJ mol^{-1})) of a few elements are given below: (e) the metal which can form a stable binary halide of the formula (MX_{2}) (X=halogen).
- Q3.31(f): The first ($\Delta_{i}H_{1}$) and the second ($\Delta_{i}H_{2}$) ionization enthalpies (in kJ $mol^{-1}$) and the ($\Delta_{eg}H$) electron gain enthalpy (in kJ $mol^{-1}$) of a few elements are given below: Elements $\Delta H_{1}$ $\Delta H_{2}$ $\Delta_{eg}H$ I 520 7300 –60 II 419 3051 –48 III 1681 3374 –328 IV 1008 1846 –295 V 2372 5251 +48 VI 738 1451 –40 Which of the above elements is likely to be : (f) the metal which can form a predominantly stable covalent halide of the formula $MX$ ($X$=halogen)?
- Q3.31(f): The first ((\Delta_{i}H_{1})) and the second ((\Delta_{i}H_{2})) ionization enthalpies (in (kJ mol^{-1})) and the ((\Delta_{eg}H)) electron gain enthalpy (in (kJ mol^{-1})) of a few elements are given below: (f) the metal which can form a predominantly stable covalent halide of the formula (MX) (X=halogen)?
- Q3.32(a): Predict the formulas of the stable binary compounds that would be formed by the combination of the following pairs of elements. (a) Lithium and oxygen
- Q3.32(a): Predict the formulas of the stable binary compounds that would be formed by the combination of the following pairs of elements. (a) Lithium and oxygen
- Q3.32(b): Predict the formulas of the stable binary compounds that would be formed by the combination of the following pairs of elements. (b) Magnesium and nitrogen
- Q3.32(b): Predict the formulas of the stable binary compounds that would be formed by the combination of the following pairs of elements. (b) Magnesium and nitrogen
- Q3.32(c): Predict the formulas of the stable binary compounds that would be formed by the combination of the following pairs of elements. (c) Aluminium and iodine
- Q3.32(c): Predict the formulas of the stable binary compounds that would be formed by the combination of the following pairs of elements. (c) Aluminium and iodine
- Q3.32(d): Predict the formulas of the stable binary compounds that would be formed by the combination of the following pairs of elements. (d) Silicon and oxygen
- Q3.32(d): Predict the formulas of the stable binary compounds that would be formed by the combination of the following pairs of elements. (d) Silicon and oxygen
- Q3.32(e): Predict the formulas of the stable binary compounds that would be formed by the combination of the following pairs of elements. (e) Phosphorus and fluorine
- Q3.32(e): Predict the formulas of the stable binary compounds that would be formed by the combination of the following pairs of elements. (e) Phosphorus and fluorine
- Q3.32(f): Predict the formulas of the stable binary compounds that would be formed by the combination of the following pairs of elements. (f) Element 71 and fluorine
- Q3.32(f): Predict the formulas of the stable binary compounds that would be formed by the combination of the following pairs of elements. (f) Element 71 and fluorine
- Q3.33: In the modern periodic table, the period indicates the value of :
- Q3.33: In the modern periodic table, the period indicates the value of :
- Q3.34: Which of the following statements related to the modern periodic table is incorrect?
- Q3.34: Which of the following statements related to the modern periodic table is incorrect?
- Q3.35: Anything that influences the valence electrons will affect the chemistry of the element. Which one of the following factors does not affect the valence shell?
- Q3.35: Anything that influences the valence electrons will affect the chemistry of the element. Which one of the following factors does not affect the valence shell?
- Q3.36: The size of isoelectronic species — $F^{-}$, $Ne$ and $Na^{+}$ is affected by
- Q3.36: The size of isoelectronic species — (F^{-}), Ne and (Na^{+}) is affected by
- Q3.37: Which one of the following statements is incorrect in relation to ionization enthalpy?
- Q3.37: Which one of the following statements is incorrect in relation to ionization enthalpy?
- Q3.38: Considering the elements $B$, $Al$, $Mg$, and $K$, the correct order of their metallic character is :
- Q3.38: Considering the elements B, Al, Mg, and K, the correct order of their metallic character is :
- Q3.39: Considering the elements $B$, $C$, $N$, $F$, and $Si$, the correct order of their non-metallic character is :
- Q3.39: Considering the elements B, C, N, F, and Si, the correct order of their non-metallic character is :
- Q3.4: On the basis of quantum numbers, justify that the sixth period of the periodic table should have 32 elements.
- Q3.4: On the basis of quantum numbers, justify that the sixth period of the periodic table should have 32 elements.
- Q3.40: Considering the elements $F$, $Cl$, $O$ and $N$, the correct order of their chemical reactivity in terms of oxidizing property is :
- Q3.40: Considering the elements F, Cl, O and N, the correct order of their chemical reactivity in terms of oxidizing property is :
- Q3.5: In terms of period and group where would you locate the element with $Z =114$?
- Q3.5: In terms of period and group where would you locate the element with (Z =114)?
- Q3.6: Write the atomic number of the element present in the third period and seventeenth group of the periodic table.
- Q3.6: Write the atomic number of the element present in the third period and seventeenth group of the periodic table.
- Q3.7(i): Which element do you think would have been named by (i) Lawrence Berkeley Laboratory
- Q3.7(i): Which element do you think would have been named by (i) Lawrence Berkeley Laboratory
- Q3.7(ii): Which element do you think would have been named by (ii) Seaborg’s group?
- Q3.7(ii): Which element do you think would have been named by (ii) Seaborg’s group?
- Q3.8: Why do elements in the same group have similar physical and chemical properties?
- Q3.8: Why do elements in the same group have similar physical and chemical properties?
- Q3.9: What does atomic radius and ionic radius really mean to you?
- Q3.9: What does atomic radius and ionic radius really mean to you?
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