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Question: Number of electrons present in 3.6 mg of NH$_{4}^{+}$ are : (N$_{A}$ = 6x10$^{23}$)...

Number of electrons present in 3.6 mg of NH4+_{4}^{+} are : (NA_{A} = 6x1023^{23})

A

1.2 x 1021^{21}

B

1.2 x 1020^{20}

C

1.2 x 1022^{22}

D

34\frac{3}{4}

E

2 x 1023^{23}

Answer

1.2 x 1021^{21}

Explanation

Solution

Here's a step-by-step explanation to calculate the number of electrons in 3.6 mg of NH4+_{4}^{+}:

  1. Calculate the molar mass of NH₄⁺:

    • Atomic mass of Nitrogen (N) = 14 g/mol
    • Atomic mass of Hydrogen (H) = 1 g/mol
    • Molar mass of NH₄⁺ = (1 × 14) + (4 × 1) = 14 + 4 = 18 g/mol

  2. Calculate the number of moles of NH₄⁺:

    • Given mass = 3.6 mg = 3.6 × 10⁻³ g
    • Number of moles = MassMolar mass\frac{\text{Mass}}{\text{Molar mass}}
    • Number of moles = 3.6×10−3 g18 g/mol=0.2×10−3 mol=2×10−4 mol\frac{3.6 \times 10^{-3} \text{ g}}{18 \text{ g/mol}} = 0.2 \times 10^{-3} \text{ mol} = 2 \times 10^{-4} \text{ mol}

  3. Calculate the number of NH₄⁺ ions:

    • Number of ions = Number of moles × Avogadro's number (NA_{A})
    • Given NA_{A} = 6 × 10²³
    • Number of ions = (2×10−4 mol)×(6×1023 ions/mol)(2 \times 10^{-4} \text{ mol}) \times (6 \times 10^{23} \text{ ions/mol})
    • Number of ions = 12×1019 ions=1.2×1020 ions12 \times 10^{19} \text{ ions} = 1.2 \times 10^{20} \text{ ions}

  4. Calculate the number of electrons in one NH₄⁺ ion:

    • Number of electrons in Nitrogen (N) = Atomic number of N = 7
    • Number of electrons in Hydrogen (H) = Atomic number of H = 1
    • Total electrons in a neutral NH₄ (hypothetical) = 7 (from N) + 4 × 1 (from 4H) = 11 electrons
    • Since it is NH₄⁺, it has lost one electron (due to the +1 charge).
    • Number of electrons in NH₄⁺ = 11 - 1 = 10 electrons

  5. Calculate the total number of electrons:

    • Total electrons = Number of NH₄⁺ ions × Number of electrons per ion
    • Total electrons = (1.2×1020 ions)×(10 electrons/ion)(1.2 \times 10^{20} \text{ ions}) \times (10 \text{ electrons/ion})
    • Total electrons = 12×1020 electrons=1.2×1021 electrons12 \times 10^{20} \text{ electrons} = 1.2 \times 10^{21} \text{ electrons}