Live practice

Principle and reasoning. Work from the governing physical relation and apply it to every stated part.

Uniform axial rotation repeats but its angular coordinate is not a linear restoring-force oscillation, so it is periodic non-SHM. A displaced U-tube column has a pressure restoring force proportional to displacement, so it is nearly SHM.

Near a smooth bowl's lowest point, the tangential restoring component is proportional to small displacement, so the ball is nearly SHM. A polyatomic molecule generally combines several normal-mode frequencies; the combined vibration is periodic or quasiperiodic but is not one SHM.

Principle and reasoning. Work from the governing physical relation and apply it to every stated part.

Contact angle is set by the competition between liquid–solid adhesion and liquid cohesion. Water adheres strongly to clean glass, so it wets and spreads with an acute angle. Mercury's cohesion dominates its adhesion to glass, so it beads with an obtuse angle.

Surface tension is energy per newly created area (or force per unit length), a material and temperature property rather than a function of how much surface already exists. Detergent lowers water's surface tension and changes the interfacial balance, improving wetting and reducing the angle.

With fixed volume and no external force, surface energy S A is least when area is least. A sphere has the minimum area for a given volume, so the drop approaches a sphere.

Principle. Young modulus is the gradient of the linear elastic portion; yielding starts where the curve ceases to remain linear.

Principle. On an x-t graph, final position gives home distance, start intercept gives departure time, slope gives speed and a crossing represents an overtake.

Principle. Convert every base unit, raising its factor to the same power carried by that unit.

Since \(n(B)=3\) and \(n(A\times B)=n(A)n(B)\),

For each structure, select the longest chain containing the maximum number of multiple bonds. Number the chain to give the multiple bonds the lowest possible locants, then identify and locate substituents.

(a) The parent chain has four carbon atoms and the double bond begins at C-2. Numbering from the right places the methyl substituent at C-2. Hence the name is 2-methylbut-2-ene.

(b) The five-carbon chain contains both a double and a triple bond. The lowest set of multiple-bond locants is 1,3, and the double bond receives the lower locant in the tie. Hence the name is pent-1-en-3-yne.

(c) The parent chain has five carbon atoms with double bonds beginning at C-1 and C-4. Hence the name is penta-1,4-diene.

(d) Number the four-carbon alkene chain from the double-bond end. The double bond begins at C-1 and the phenyl group is attached at C-4. Hence the name is 4-phenylbut-1-ene.

(e) The hydroxyl group defines phenol as the parent and occupies C-1. The methyl group is on the adjacent carbon, C-2. Hence the name is 2-methylphenol.

(f) The longest continuous chain contains ten carbon atoms. A 2-methylpropyl substituent is attached at C-5. Hence the name is 5-(2-methylpropyl)decane.

(g) The parent chain has ten carbon atoms and three double bonds at C-1, C-5 and C-8; the ethyl substituent is at C-4. Hence the name is 4-ethyldeca-1,5,8-triene.

Count one sigma bond between each connected atom; a double bond adds one pi bond and a triple bond adds two.

Apply the oxidation-number sum rule. Fractional results are average oxidation states caused by equivalent/non-equivalent atoms or mixed valency.

Insert equilibrium concentrations into the mass-action expression.