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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 $J mol^{-1}$.
Solution :
Step 1: Theoretical Foundation of Ionization Enthalpy
The ionization enthalpy ($IE$) 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. Mathematically, for a hydrogen atom, this corresponds to the energy required to transition an electron from the ground state ($n=1$) to an infinite distance from the nucleus ($n=\infty$), where the potential energy of the electron is defined as zero.
The energy change ($\Delta E$) is expressed as:
$\Delta E = E_{\infty} - E_{ground}$
[Per the Bohr model of the hydrogen atom, where $E_{\infty} = 0$ J]
Step 2: Calculation of Energy for One Mole of Atoms
Given the energy of an electron in the ground state of a single hydrogen atom ($E_1$):
$E_1 = -2.18 \times 10^{-18} \, J$
The energy required to ionize one hydrogen atom is:
$\Delta E = 0 - (-2.18 \times 10^{-18} \, J) = +2.18 \times 10^{-18} \, J$
[Justification: By the Principle of Conservation of Energy, the energy absorbed must equal the difference between the final and initial states.]
Step 3: Conversion to Molar Enthalpy
To calculate the ionization enthalpy in terms of $J \, mol^{-1}$, we must multiply the energy per atom by the Avogadro constant ($N_A$), which represents the number of atoms in one mole ($6.022 \times 10^{23} \, mol^{-1}$).
$IE = \Delta E \times N_A$
$IE = (2.18 \times 10^{-18} \, J \cdot atom^{-1}) \times (6.022 \times 10^{23} \, atom \cdot mol^{-1})$
Step 4: Algebraic Evaluation
Executing the multiplication of the coefficients and the exponents:
- Coefficient product: $2.18 \times 6.022 \approx 13.12796$
- Exponent sum: $10^{-18} \times 10^{23} = 10^{5}$
$IE = 13.12796 \times 10^5 \, J \, mol^{-1}$
Normalizing to scientific notation:
$IE = 1.312796 \times 10^6 \, J \, mol^{-1}$
Final Solution: The ionization enthalpy of atomic hydrogen is $1.31 \times 10^6 \, J \, mol^{-1}$.
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 \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.
- Q3.25: 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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