4
Problem solving
Textbook: pp. 16–17
GoalSolve problems on amount of substance, number of molecules, mass and concentration step by step.
New words
density · zichlikconcentration · konsentratsiyaGiven – Formula – Calculation · Berilgan – Formula – Hisoblashunit check · o‘lchamlik tekshiruvi
Explanation
When solving a problem, first convert the givens into SI units (g → kg, cm³ → m³), then pick the formula. The chain for finding a number of molecules is usually: mass → amount of substance ν = m/M → number of molecules N = νN_A. If a volume is given, first find the mass m = ρV. The concentration is n = N/V, with the volume in m³. At the end check the units: for example mol·mol⁻¹ gives a pure number. Take N_A = 6.02·10²³ mol⁻¹ and round the answer to 2–3 significant figures.
Worked examples
Number of atoms in 0.6 g of diamond (carbon, M = 12 g/mol): ν = 0.6/12 = 0.05 mol; N = νN_A = 0.05·6.02·10²³ ≈ 3·10²².
Number of atoms in a 1 cm³ copper cube (ρ = 8900 kg/m³ = 8.9 g/cm³, M = 64 g/mol): m = ρV = 8.9 g; ν = 8.9/64 ≈ 0.139 mol; N = 0.139·6.02·10²³ ≈ 8.4·10²².
Class activity
“Chain” game in groups of three: one person gets a mass, the second finds ν, the third finds N; write every step in the notebook and then swap roles. A calculator may be used to check.
Practice
1
Find the mass of one water molecule (M = 18·10⁻³ kg/mol).
3.0·10⁻²⁶ kg
2
Find the number of molecules in 4 g of hydrogen H₂ (M = 2 g/mol).
1.2·10²⁴
3
A vessel holds 2.408·10²⁴ molecules. What is the amount of substance? (N_A = 6.02·10²³ mol⁻¹)
4 mol
4
Why must the volume first be converted to m³ in the problem?
Because density is in kg/m³ and concentration in m⁻³; mixing units gives a wrong result.