Live practice

(a) \(\ce{H3C-C(=O)-O-H}\); each O has two lone pairs. (b) \(\ce{H-S-H}\); S has two lone pairs. (c) \(\ce{CH3-C(=O)-CH3}\); O has two lone pairs. (d) \(\ce{F-F}\); each F has three lone pairs.

In every case a line represents one shared electron pair. Counting shared and lone pairs gives a duplet for H and an octet for C, O, S and F.

A high melting point indicates an ionic oxide. Calcium is a metal and forms ionic calcium oxide, which reacts with water to produce calcium hydroxide:

On heating, sodium hydrogencarbonate decomposes to sodium carbonate, carbon dioxide and water:

Effervescence is due to carbon dioxide. The gas turns lime water milky.

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

Pressure variation is proportional to the spatial gradient of particle displacement. Displacement is zero with the steepest gradient at a displacement node, giving a pressure antinode; at a displacement antinode the gradient and pressure variation vanish.

Bats emit ultrasound and analyse echo delay, arrival direction, intensity, and spectrum to infer range, direction, size, and texture. Violin and sitar have different harmonic amplitudes and transients, so their timbres differ despite equal fundamentals.

Solids possess both bulk and shear elasticity, supporting compression and shear restoring forces. Gases have essentially no static shear modulus, so only longitudinal pressure waves propagate. In a dispersive medium different Fourier components travel at different speeds, changing their relative phases and hence the pulse shape.

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

Kirchhoff's law equates emissivity and absorptivity at thermal equilibrium; a strong reflector absorbs little and therefore emits poorly. Brass conducts heat from the hand much faster than wood, so it feels colder at the same temperature.

Exposed iron has emissivity below one, hence radiates less than a black body at the same temperature and a black-body calibration reads low. In a furnace cavity, repeated absorption and reflection make the radiation field nearly black-body radiation at the furnace temperature.

The atmosphere absorbs and returns part of Earth's outgoing infrared radiation, raising surface temperature. Steam releases a large latent heat when it condenses as well as sensible heat, so each kilogram transfers much more energy than hot water.

Principle. Normalize the two diagonal directions and project A onto their unit vectors.

Define the sample space and count each favourable outcome once.

The final value lies in [0,1]; complement pairs also sum to one, providing an independent check.

Form the required totals explicitly and divide by the full number of observations.

The variance is nonnegative and the reported standard deviation is its positive square root.

Simplify the expression before substitution and preserve one-sided information.

Substitution into the original expression verifies the stated domain and final value.

Translate every condition into an equation and retain exact values throughout the conic calculation.

The last line satisfies the original conditions and supplies every requested part.