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Hess's Law and Waves

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Hess's Law and Waves

You are checking two different kinds of physics and chemistry data for a science exhibition. Work through the energy-cycle and wave investigations. Show calculations with units and use significant figures sensibly.

A. Hess's Law: energy routes

Enthalpy is a state function: the enthalpy change between fixed initial and final states is independent of the route. Use the supplied reaction data to calculate unknown changes. Reverse an equation by changing the sign of ΔH; multiply an equation by a factor by multiplying ΔH by the same factor.

1.A student says, “If a reaction takes a different route, its enthalpy change must be different.” Choose the best correction.

The student is right: enthalpy depends on the reaction mechanism.
The student is wrong: ΔH depends only on the initial and final states, not the route.
The student is right unless the reaction is carried out at constant pressure.
Hess's Law applies only when a reaction has one step.

2.Use these equations to find ΔH for C(s) + ½O₂(g) → CO(g): (1) C(s) + O₂(g) → CO₂(g), ΔH = −394 kJ mol⁻¹; (2) CO(g) + ½O₂(g) → CO₂(g), ΔH = −283 kJ mol⁻¹. Show how you combine the equations.

3.A data logger gives two routes from A to D: A → B has ΔH = +42 kJ mol⁻¹ and B → D has ΔH = −17 kJ mol⁻¹; A → C has ΔH = −8 kJ mol⁻¹ and C → D has ΔH = x. Find x, assuming both routes connect the same states.

4.For the formation of methane, C(s) + 2H₂(g) → CH₄(g), use ΔH°c[CH₄] = −890 kJ mol⁻¹, ΔH°c[C] = −394 kJ mol⁻¹ and ΔH°c[H₂] = −286 kJ mol⁻¹. Calculate ΔH°f[CH₄].

B. Stationary waves: the sound lab

A stationary wave forms when two waves of the same frequency and similar amplitude travel in opposite directions and superpose. Nodes have zero displacement; antinodes have maximum displacement. In a stationary wave, there is no net energy transfer along the medium.

5.A stationary wave on a string has three loops between its fixed ends. A loop is the section between two neighbouring nodes. There is a node at each end and at every point where neighbouring loops meet, with one antinode in each loop. How many nodes and antinodes are there? State the spacing between neighbouring nodes in terms of wavelength λ.

6.Select the two statements that correctly describe a stationary wave.

Every point on the string has the same amplitude.
Nodes remain at fixed positions.
The wave transfers energy steadily from one end to the other.
Adjacent nodes are separated by half a wavelength.

7.A string fixed at both ends is 1.20 m long and vibrates in its third harmonic. The wave speed is 240 m s⁻¹. Calculate (a) its wavelength, (b) its frequency and (c) the number of nodes, including the fixed ends.

8.A stationary wave is not an example of “path-independent energy change” in the same sense as Hess's Law. Explain why the comparison is limited, and state one valid similarity between the ideas.