NEET 2.0 Physical Chemistry - Atomic and Molecular Mass Study Notes

Recap of Atomic Structure

• Atom Representation: An atom or ion is typically represented as ${}_{Z}^{A}X$.

  • $A$: Mass Number (Total number of nucleons: protons + neutrons).

  • $Z$: Atomic Number (Total number of protons).

• Subatomic Particles Calculation:

  • Number of Protons ($p$) = $Z$.

  • Number of Neutrons ($n$) = $A - Z$.

  • Number of Electrons ($e$):

    • In a neutral atom: $e = p = Z$.

    • In a cation (positive ion): electrons are lost ($e = Z - \text{charge}$).

    • In an anion (negative ion): electrons are gained ($e = Z + |\text{charge}|$).

• Example Calculations (Sulfur Species):

  • For ${}_{16}^{32}S^{2-}$:

    • $p = 16$

    • $n = 32 - 16 = 16$

    • $e = 16 + 2 = 18$

• Charge Details:

  • Exact charge of 1 electron/proton = $1.6 \times 10^{-19}\,\text{Coulombs}$.

  • Relative charge of 1 proton is considered $+1$. If a species has an excess of one proton relative to electrons, its relative charge is $+1$.

Classification of Atomic Species

• Isotopes: atoms of the same element having the same number of protons (Atomic Number $Z$) but different number of neutrons (and thus different Mass Number $A$).

• Isobars: Atoms of different elements having the same Mass Number ($A$) but different Atomic Numbers ($Z$).

• Isotones: Species having the same number of neutrons ($n = A - Z$).

• Isodiaphers: Species having the same value of $(n - p)$ or $(A - 2Z)$.

• Isoelectronic: Species (atoms, ions, or molecules) having the same total number of electrons ($e$).

• Isosters: Species having the same atomicity (total number of atoms) and the same total number of electrons.

Practice Problems: Atomic and Subatomic Species

• Q.1: Relation between ${}_{6}^{13}C$ and ${}_{8}^{17}O$:

  • For ${}_{6}^{13}C$: $p = 6$, $n = 13 - 6 = 7$, $e = 6$. Calculation: $n - p = 7 - 6 = 1$.

  • For ${}_{8}^{17}O$: $p = 8$, $n = 17 - 8 = 9$, $e = 8$. Calculation: $n - p = 9 - 8 = 1$.

  • Conclusion: Since they have the same $(n - p)$ value, they are isodiaphers.

• Q.2: Identification of species with 16 protons, 18 electrons, and 16 neutrons:

  • 16 protons identify the element as Sulfur ($S$).

  • Electrons (18) are 2 more than protons (16), indicating a charge of $-2$.

  • Identity: $S^{2-}$.

• Q.3: Representation of a diatomic gas molecule ($A_2$) containing 32 electrons and 36 neutrons:

  • For molecule $A_2$: Total $e = 32$, Total $n = 36$.

  • Per atom of $A$: $e = 16$, $n = 18$.

  • Atomic number $Z = p = e = 16$.

  • Mass number $A = p + n = 16 + 18 = 34$.

  • Representation: ${}_{16}^{34}A$.

• Q.4: Neutron percentage in an imaginary ion ${}_{22}^{48}Y^{3-}$:

  • Number of protons ($p$) = 22.

  • Number of electrons ($e$) = $22 + 3 = 25$.

  • Number of neutrons ($n$) = $48 - 22 = 26$.

  • Difference between neutrons and electrons = $26 - 25 = 1$.

  • Percentage of more neutrons than electrons ($x\%$): $\frac{26 - 25}{25} \times 100 = 4\%$.

• Q.5: Composition of the nitride ion in Lithium Nitride ($Li_3N$):

  • The nitride ion is $N^{3-}$.

  • For Nitrogen (${}_{7}^{14}N$): Protons = 7, Neutrons = $14 - 7 = 7$.

  • For $N^{3-}$ ion: Electrons = $7 + 3 = 10$.

  • Composition: 7 protons + 10 electrons.

• Q.6: Neutrons in tripositive Aluminum ion ($Al^{3+}, A=27$):

  • Atomic number of Aluminum is 13.

  • Number of neutrons = $27 - 13 = 14$.

Conceptual Identification Exercises

• Isotope Characteristics:

  • Isotopes have the same number of protons.

  • They have different mass numbers and different numbers of neutrons.

• Identifying Non-Isotope Pairs:

  • Pair ${}_{6}^{12}Y, {}_{6}^{13}Y$: Isotopes (Same $\text{Atomic No.}$).

  • Pair ${}_{17}^{35}X, {}_{17}^{33}Y$: Isotopes (Same $\text{Atomic No.}$).

  • Pair ${}_{6}^{14}X, {}_{7}^{14}Y$: Not isotopes (They are isobars, as they have the same mass number 14).

• Isoelectronic Ion Pairs:

  • $Na^{+}$ ($11 - 1 = 10e$) and $Mg^{2+}$ ($12 - 2 = 10e$) are isoelectronic.

  • $Al^{3+}$ ($13 - 3 = 10e$) and $O^{2-}$ ($8 + 2 = 10e$) are isoelectronic.

Average Atomic Mass (A.A.M)

• Definition: Average Atomic Mass is defined for elements that exist as multiple isotopes in nature. It depends on the relative abundance of these isotopes in the universe.

• Mathematical Formula:     $A.A.M = \frac{\sum (\text{Isotopic Mass} \times \text{\% Abundance})}{100}$     Alternatively, if given ratios: $A.A.M = \frac{\sum (\text{Isotopic Mass} \times \text{Ratio weight})}{\sum \text{Ratios}}$.

• Key Distinction:

  • Mass Number: Always a whole number (count of nucleons).

  • Atomic Mass / Molar Mass / Average Atomic Mass: Can be fractional numbers.

• Example 1 (Abundance percentages):

  • Element Z exists as isotopes $Z^{40}$ (20%), $Z^{45}$ (30%), and $Z^{50}$ (50%).

  • $A.A.M = \frac{40 \times 20 + 45 \times 30 + 50 \times 50}{100}$

  • $A.A.M = \frac{800 + 1350 + 2500}{100} = \frac{4650}{100} = 46.5$

• Example 2 (Abundance ratios):

  • Element X exists as isotopes $X^{15}$ and $X^{18}$ in the ratio 2:3.

  • Calculation via percentage: $\text{\% } X^{15} = \frac{2}{2+3} \times 100 = 40\%$, $\text{\% } X^{18} = \frac{3}{5} \times 100 = 60\%$.

  • $A.A.M = \frac{15 \times 40 + 18 \times 60}{100} = \frac{600 + 1080}{100} = 16.8$

• Example 3 (Finding percentage abundance):

  • Element Y has $A.A.M = 20$ and exists as isotopes $Y^{18}$ and $Y^{25}$.

  • Let abundance of $Y^{18}$ be $x\%$, then $Y^{25}$ is $(100 - x)\%$.

  • $20 = \frac{18x + 25(100 - x)}{100}$

  • $2000 = 18x + 2500 - 25x$

  • $7x = 500 \rightarrow x = \frac{500}{7} \approx 71.4\%$

Atomic Mass and Units

• Subatomic Particle Masses:

  • Mass of proton ($m_p$) = $1.67 \times 10^{-27}\,\text{kg} = 1.67 \times 10^{-24}\,\text{g}$.

  • Mass of neutron ($m_n$) = $1.67 \times 10^{-27}\,\text{kg} = 1.67 \times 10^{-24}\,\text{g}$.

  • Mass of electron ($m_e$) = $9.1 \times 10^{-31}\,\text{kg}$ (often neglected in atomic mass calculations as it is $\approx \frac{1}{1837}$ times the mass of a proton).

• Atomic Mass Unit (a.m.u. or u):

  • Defined as exactly $\frac{1}{12}$th of the mass of one atom of Carbon-12 (${}^{12}C$).

  • $1\,\text{a.m.u} = m_p = m_n = 1.67 \times 10^{-24}\,\text{g}$.

• Mass of 1 atom of an element:

  • $\text{Mass of 1 atom} = (\text{Mass Number } A) \times 1.67 \times 10^{-24}\,\text{g}$.

  • $\text{Mass of 1 atom} = A\,\text{a.m.u.}$

  • Example: For ${}_{8}^{16}O$, mass of 1 atom = $16\,\text{a.m.u} \approx 16 \times 1.67 \times 10^{-27}\,\text{kg}$.

• Calculations using a.m.u:

  • Number of atoms = $\frac{\text{Given mass of element (a.m.u)}}{\text{Atomic mass of element (a.m.u)}}$.

  • Example: Number of Nitrogen atoms in 280 a.m.u:

    • Atomic mass of N = $14\,\text{a.m.u}$.

    • $\text{Atoms} = \frac{280}{14} = 20\,\text{atoms}$.

Molecular Mass

• Definition: The sum of the atomic masses of all atoms present in a molecule.

• Examples:

  • Oxygen Gas ($O_2$): Mass of 1 molecule = $16 \times 2 = 32\,\text{a.m.u}$.

  • Water ($H_2O$): Mass of 1 molecule = $(1 \times 2) + 16 = 18\,\text{a.m.u}$.

  • Nitric Acid ($HNO_3$):

    • Mass = $1 + 14 + (16 \times 3) = 63\,\text{a.m.u}$.

    • Electrons = $1 + 7 + (8 \times 3) = 32$.

    • Protons = $1 + 7 + (8 \times 3) = 32$.

    • Neutrons = $0 + 7 + (8 \times 3) = 31$.

• Example Calculation: How many molecules of $H_2SO_4$ are in 980 a.m.u of mass?

  • Molecular mass of $H_2SO_4 = (1 \times 2) + 32 + (16 \times 4) = 2 + 32 + 64 = 98\,\text{a.m.u}$.

  • $\text{Number of molecules} = \frac{980\,\text{a.m.u}}{98\,\text{a.m.u}} = 10\,\text{molecules}$.

Unit Conversions and Scales

• Mass Conversions:

  • $1\,\text{kg} = 10^{3}\,\text{g}$.

  • $1\,\text{g} = 10^{-3}\,\text{kg}$.

  • $1\,\mu\text{g} = 10^{-6}\,\text{g}$.

  • $1\,\text{mg} = 10^{-3}\,\text{g}$.

• Distance/Length Conversions:

  • $1\,\text{nanometer (nm)} = 10^{-9}\,\text{meter}$.

  • $1\,\text{meter} = 10^{9}\,\text{nm}$.

• Mass vs a.m.u Relationship:

  • $1\,\text{a.m.u} = 1.67 \times 10^{-24}\,\text{g}$.

  • $1\,\text{gram} = \frac{1}{1.67 \times 10^{-24}}\,\text{a.m.u}$.

  • Example: $8\,\text{g} = \frac{8}{1.67 \times 10^{-24}}\,\text{a.m.u}$.