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Practical work and problems

Lessons 13–14 · 2 lessons · P. Habibullayev, A. Boydedayev, A. Bahromov, K. Suyarov, J. Usarov, M. Yuldasheva. Physics Grade 9, revised and expanded 3rd edition. G‘afur G‘ulom Publishing House, Tashkent, 2019
13

Practical work: estimating the size of molecules

Textbook: pp. 38–39
GoalUnderstand how a mechanical model (peas) can estimate molecule size; calculate the density, concentration and mass of the air in a room.
New words
mechanical model · mexanik modelmeasurement error · o‘lchash xatoligianeroid barometer · aneroid barometrroom volume · xona hajmi
Explanation

In the oil-film method the molecule size is estimated by d = V/S. To test the idea, a mechanical model is used: dry peas instead of molecules. Draw a rectangle on white paper and measure its area S, cover it with a single tight layer of peas, pour the peas into a measuring cylinder to find the volume V, and compute d = V/S. Compare with a direct measurement: place 10 peas in a tight row and divide the length by 10. The difference comes from gaps between peas and measurement error. Second part: with an aneroid barometer measure the room pressure and with a thermometer the temperature, then find ρ = pM/(RT), n = p/(kT), N = nV and m = ρV (for air M = 0.029 kg/mol).

Worked examples
Example (approximate numbers; replace with your own): S = 20 cm × 15 cm = 300 cm², V = 150 cm³ gives d = V/S = 0.5 cm. Direct measurement: 10 peas = 6.5 cm, so d ≈ 0.65 cm. The difference: gaps between peas distort the measured volume V.
Let the room be 6 m × 5 m × 3 m, p = 10⁵ Pa, T = 300 K. V = 90 m³; ρ = pM/(RT) = 10⁵·0.029/(8.31·300) ≈ 1.16 kg/m³; m = ρV ≈ 105 kg; n = p/(kT) ≈ 2.4·10²⁵ m⁻³; N = nV ≈ 2.2·10²⁷.
Class activity

Practical: groups of 4–5 measure d with the pea model, enter the results in a table on the board and find the mean. Afterwards collect the peas. Handle the barometer and thermometer carefully; if a mercury thermometer breaks, do not touch it and tell the teacher at once.

Practice
1
Which formula gives the thickness in the oil-film method and in the pea model?
2
120 cm³ of peas fill a single layer over 240 cm². What is the layer thickness?
3
A classroom is 8 m × 6 m × 3 m. What is the room volume in m³?
4
Why does the d from the pea model usually differ from the real diameter?