Question 14 of 17intermediate🔧 ApplyNumerical2 marks

The unit of length convenient on the atomic scale is known as an angstrom and is denoted by Å: 1 Å = 10⁻¹⁰ m. The size of a hydrogen atom is about 0.5 Å. What is the total atomic volume in m³ of a mole of hydrogen atoms?

Correct Answer

The total atomic volume of a mole of hydrogen atoms is approximately 3×103 \times 10⁻⁷ m³.

Exercise: EXERCISES | Q: 1.14 | (Page 11)
For More Understanding

Explanation

This question tests understanding of atomic dimensions and mole concept. The size given (0.5 Å) refers to the radius of the hydrogen atom. The volume of a single atom is calculated using the sphere formula, then multiplied by Avogadro's number to get the total volume for one mole.

Solution Steps

  1. Step 1: Convert the size of hydrogen atom from angstrom to meters. Size of hydrogen atom = 0.5 Å = 0.5×100.5 \times 10⁻¹⁰ m = 5×105 \times 10⁻¹¹ m This is the radius (r) of the hydrogen atom.

  2. Step 2: Calculate the volume of one hydrogen atom (assuming spherical shape). Volume of one atom = (4/3)πr³ V = (4/3) × π × (5×105 \times 10⁻¹¹)³ V = (4/3) × π × 125×10125 \times 10⁻³³ V ≈\approx 5.24×105.24 \times 10⁻³¹ m³

  3. Step 3: Calculate total atomic volume for one mole of hydrogen atoms. One mole contains Avogadro's number of atoms (N_A = 6.022×106.022 \times 10²³ atoms). Total atomic volume = Volume of one atom × N_A V_total = 5.24×105.24 \times 10⁻³¹ × 6.022×106.022 \times 10²³ V_total ≈\approx 3.16×103.16 \times 10⁻⁷ m³ ≈\approx 3×103 \times 10⁻⁷ m³

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