AP Chemistry FRQ Practice

🧪AP Chemistry

Practice FRQ 1 of 351/35

3. Answer the following questions about calcium and its compounds.

The mass spectrum of a pure sample of calcium is shown in Figure 1. The spectrum indicates the relative intensities of the naturally occurring isotopes.

Figure 1. Mass spectrum of calcium (relative isotopic intensities; most abundant isotope normalized to 100.0)

Create a clean, black-and-white stick-spectrum style bar graph (mass spectrum).

Overall layout:
- The plot is rectangular and centered on the page with a single set of axes. No title text inside the plotting area.
- No gridlines.

Axes:
- Horizontal axis label centered below the axis: "Isotopic Mass (amu)".
- Horizontal axis numeric range: from 38 to 46 inclusive.
- Show tick marks and printed tick labels at every integer mass value: 38, 39, 40, 41, 42, 43, 44, 45, 46.
- Vertical axis label rotated vertically along the left side: "Relative Intensity".
- Vertical axis numeric range: from 0 to 100.
- Show tick marks and printed tick labels at 0, 20, 40, 60, 80, and 100.
- Axes lines are solid black with arrowheads at the positive ends (right end of x-axis, top end of y-axis).

Spectrum peaks (must be exactly two peaks; all other masses have zero intensity):
- Use very thin, vertical, solid black lines (stick peaks), each centered exactly on its integer mass value.
- Peak 1 (dominant): at mass 40, a vertical line rising from the baseline at y=0 to the top tick at y=100. The top of this line aligns exactly with the y-axis tick labeled 100.
- Peak 2 (minor): at mass 44, a vertical line rising from the baseline at y=0 to y=2.1 on the same y-axis scale. Since 2.1 is just above the baseline and far below the 20 tick, ensure the peak height is visibly slightly above y=0 but clearly much less than one-tenth of the distance to the 20 tick.

Numerical annotations (visible text in the figure):
- Place the text "100.0" directly above the top of the mass-40 peak, centered over that peak.
- Place the text "2.1" directly above the top of the mass-44 peak, centered over that peak.

Zero-intensity requirement:
- At masses 38, 39, 41, 42, 43, 45, and 46, there are no vertical lines or bars at all (blank baseline only).

i. Determine the number of neutrons in the most abundant isotope of calcium shown in Figure 1.

ii. Using the data in Figure 1, calculate the average atomic mass of the calcium sample to two decimal places. Show your work.

A student heats a sample of calcium in a crucible containing nitrogen gas. The calcium reacts with the nitrogen to form a pure ionic compound. The student records the data shown in Table 1.

Table 1. Experimental data for the reaction of calcium with nitrogen

Measurement	Mass (g)
Mass of empty crucible	22.000
Mass of crucible + calcium	23.203
Mass of crucible + final compound	23.483

i. Calculate the number of moles of calcium that reacted.

ii. Calculate the empirical formula of the compound formed. Show your work.

The complete photoelectron spectrum (PES) of calcium is shown in Figure 2.

Figure 2. Photoelectron spectrum (PES) of calcium (binding energy on a logarithmic axis decreasing left to right)

Create a black-and-white photoelectron spectrum with six peaks.

Overall layout:
- A single rectangular plotting area with one set of axes.
- No gridlines.
- Peaks drawn as smooth, symmetric, narrow bell-shaped curves (Gaussian-like), not spikes and not bars.
- All peaks start at the baseline, rise to a single apex, and return to the baseline.

Axes:
- Horizontal axis label centered below the axis: "Binding Energy (MJ/mol)".
- Horizontal axis is logarithmic and reversed (values decrease from left to right).
- The leftmost printed tick label is "1000" and the rightmost printed tick label is "0.1".
- Print tick labels at: 1000, 100, 10, 1, 0.1 (evenly spaced by decades in log space). Include minor tick marks between decades (unlabeled) to visually reinforce the log scale.
- Vertical axis label along the left side: "Relative Number of Electrons".
- Vertical axis baseline is labeled "0" at the origin. The axis should extend high enough to clearly show a peak height of 6.
- Print y-axis tick labels at 0, 1, 2, 3, 4, 5, and 6.

Peak positions and relative heights (six total, ordered from left to right):
Because the x-axis is logarithmic and reversed, the left side corresponds to the largest binding energies.

1) Leftmost peak (highest binding energy):
- Center the peak exactly at 390 MJ/mol.
- Peak height exactly 2 on the y-axis scale (apex aligns with the y tick labeled 2).

2) Second peak from the left:
- Center the peak exactly at 44 MJ/mol.
- Peak height exactly 2.

3) Third peak from the left:
- Center the peak exactly at 35 MJ/mol.
- Peak height exactly 6 (apex aligns with the y tick labeled 6).
- This peak must be three times taller than the peaks of height 2.

4) Fourth peak from the left:
- Center the peak exactly at 4.8 MJ/mol.
- Peak height exactly 2.

5) Fifth peak from the left:
- Center the peak exactly at 2.9 MJ/mol.
- Peak height exactly 6.

6) Rightmost peak (lowest binding energy):
- Center the peak exactly at 0.59 MJ/mol.
- Peak height exactly 2.

Spacing / ordering constraints (to prevent numerical drift):
- Ensure the left-to-right order of peak centers is strictly: 390, then 44, then 35, then 4.8, then 2.9, then 0.59 MJ/mol.
- The 44 and 35 MJ/mol peaks must appear close together compared with the large gap between 390 and 44 (consistent with a log axis): visually, the 44 and 35 peaks should be in the same decade (between 10 and 100) and separated by a small horizontal distance, while 390 is in the 100–1000 decade and noticeably farther left.
- The 4.8 and 2.9 peaks must be in the 1–10 decade, with 4.8 left of 2.9.
- The 0.59 peak must be in the 0.1–1 decade near the right side.

Line styles:
- Axes: solid black, medium thickness, with arrowheads at the positive ends (right end of x-axis, top end of y-axis).
- Peaks: solid black, thin-to-medium thickness, identical width/shape for all peaks so that only height and horizontal position differ.

No extra text:
- Do not label subshells (e.g., 1s, 2p) on the graph.
- Do not add a legend.
- Only show axis labels and tick values.

i. Write the complete ground-state electron configuration for the calcium atom.

ii. Based on the electron configuration, identify the peak in Figure 2 that corresponds to the electrons in the 3s sublevel. Justify your answer in terms of relative energy and number of electrons.

i. The first ionization energy of calcium is 590 kJ/mol, while the first ionization energy of potassium is 419 kJ/mol. Explain this difference using principles of atomic structure.

ii. Predict whether the second ionization energy of calcium is greater than, less than, or equal to the second ionization energy of potassium. Justify your answer.

E. Explain why the ionic radius of the calcium ion, Ca²⁺, is smaller than the ionic radius of the sulfide ion, S²⁻, even though they are isoelectronic.

F. The lattice energy of CaO(s) is -3414 kJ/mol, whereas the lattice energy of K₂O(s) is -2238 kJ/mol. Explain this difference using Coulomb's law.