AP Chemistry FRQ Practice

🧪AP Chemistry

Practice FRQ 1 of 351/35

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

Titanium is a transition metal with atomic number 22. It is widely used in aerospace applications due to its high strength-to-weight ratio and resistance to corrosion.

Figure 1. Mass spectrum of titanium (isotopic abundances used for average atomic mass calculation)

Single-panel bar graph with five vertical bars.

Overall layout:
- White background, no gridlines.
- Plot area is a rectangle occupying most of the figure with a small margin for axis labels.

Axes (must be explicit and numerically labeled):
- Horizontal axis label centered below the axis: "Mass Number".
- Horizontal axis spans mass numbers from 45 to 51.
- Horizontal tick marks and tick labels appear at every integer: 45, 46, 47, 48, 49, 50, 51.
- Vertical axis label rotated and centered along the left side: "Percent Abundance (%)".
- Vertical axis starts at 0 and ends at 80.
- Vertical tick marks and tick labels appear every 10 units: 0, 10, 20, 30, 40, 50, 60, 70, 80.
- Both axes have arrowheads at the positive ends (right end of x-axis, top end of y-axis).

Bars (exact numerical heights; bars are centered on integer mass numbers):
- Five bars only, located exactly at mass numbers 46, 47, 48, 49, and 50 (no bar at 45 or 51).
- Each bar has identical width (each bar is narrow enough that there is visible white space between adjacent bars).
- All bars begin at the y=0 baseline.
- Bar at mass number 46 reaches exactly 8.0 on the y-axis.
- Bar at mass number 47 reaches exactly 7.3 on the y-axis.
- Bar at mass number 48 reaches exactly 73.8 on the y-axis (this is the tallest bar and rises to just below the 80 tick).
- Bar at mass number 49 reaches exactly 5.5 on the y-axis.
- Bar at mass number 50 reaches exactly 5.4 on the y-axis.

Value labeling (to force exactness):
- Above the top of each bar, centered horizontally over that bar, print the exact percent value as text:
- Above mass 46 bar: "8.0%"
- Above mass 47 bar: "7.3%"
- Above mass 48 bar: "73.8%"
- Above mass 49 bar: "5.5%"
- Above mass 50 bar: "5.4%"

Ordering/relative appearance constraints:
- The bar at 48 is dramatically taller than all others.
- Among the four shorter bars, the 46 bar is the tallest, then 47, then 49, then 50 (49 and 50 are nearly equal but 49 is visibly slightly taller than 50).

Styling:
- Bars are solid medium-gray with black outlines.
- Axes are black, medium thickness.
- No legend.

Calculate the average atomic mass of titanium using the isotopic abundance data provided in Figure 1. Show your work.

Write the complete ground-state electron configuration for a neutral titanium atom.

Figure 2. Photoelectron spectrum of titanium (valence region): binding energy and relative peak intensities

Single-panel photoelectron spectrum with four labeled peaks (A, B, C, D).

Overall layout:
- White background, no gridlines.
- Plot area is a rectangle with margins for axis titles and tick labels.

Axes (must be explicit and numerically labeled):
- Horizontal axis label centered below the axis: "Binding Energy (MJ/mol)".
- The binding energy axis is reversed: the left end is 10 and the right end is 0.
- Horizontal tick marks and tick labels appear at every 1 MJ/mol: 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0.
- Vertical axis label rotated and centered along the left side: "Relative Intensity".
- Vertical axis starts at 0 and ends at 3.
- Vertical tick marks and tick labels are exactly: 0, 1, 2, 3.
- Both axes have arrowheads at the positive ends (rightward arrow on the x-axis is NOT used because the scale is reversed; instead, place a small text note near the x-axis label reading: "(scale decreases left right)" to unambiguously indicate direction). The y-axis has an upward arrowhead.

Spectrum trace and peak shape:
- Use a thin black baseline along y=0 across the entire x-range.
- Peaks are drawn as narrow, symmetric triangular spikes (not rounded), each rising from the baseline and returning to the baseline, to make peak centers unambiguous.
- Each peak’s apex is directly above its stated binding energy value.

Exact peak positions (left to right on the page because x-axis is reversed):
- Peak A: apex at binding energy 5.5 MJ/mol with peak height exactly 1 on the relative intensity axis.
- Peak B: apex at binding energy 3.9 MJ/mol with peak height exactly 3 on the relative intensity axis.
- Peak C: apex at binding energy 0.76 MJ/mol with peak height exactly 1 on the relative intensity axis.
- Peak D: apex at binding energy 0.59 MJ/mol with peak height exactly 1 on the relative intensity axis.

Peak order constraint (must match reversed axis):
- Because 10 is on the left and 0 is on the right, the peaks must appear in this left-to-right order across the page: A (5.5), then B (3.9), then C (0.76), then D (0.59).
- Peaks C and D must be clustered near the far-right end of the axis, with D slightly to the right of C.

Peak labels and numeric annotations (to force exactness):
- Place a bold letter label centered above each apex: "A", "B", "C", "D".
- Directly below each apex (slightly above the baseline so it does not overlap the axis), print the binding energy as text:
- Under A: "5.5"
- Under B: "3.9"
- Under C: "0.76"
- Under D: "0.59"
- Next to the y-axis (or in a small note inside the plot area), add: "Peak heights: A=1, B=3, C=1, D=1".

Styling:
- Peaks and axes in black.
- Peak B is visibly three times the height of peaks A, C, and D (which are equal height).
- No legend, no additional peaks, no title inside the plot area.

The photoelectron spectrum in the range of 0 to 10 MJ/mol for titanium is shown in Figure 2.

Identify the subshell corresponding to Peak B in Figure 2. Justify your answer based on the relative height of the peaks.

ii.

Explain why Peak C has a higher binding energy than Peak D, even though the electrons in subshell C are added after the electrons in subshell D during the Aufbau filling process.

Table 1. Experimental data for the reaction of titanium with chlorine

Measurement	Mass (g)
Mass of empty crucible	25.00
Mass of crucible + titanium	26.44
Mass of crucible + titanium chloride product	29.63

Calculate the empirical formula of the titanium chloride compound formed. Show your work. A student heats the 1.44 g sample of titanium powder in an excess of chlorine gas, $Cl_2(g)$ , to form a solid titanium chloride compound. The data are recorded in Table 1.

The student performs the experiment again but stops heating before all the titanium has reacted. Would the calculated ratio of moles of Cl to moles of Ti be greater than, less than, or equal to the actual ratio in the compound? Justify your answer.

Write the complete ground-state electron configuration for the $Ti^{2+}$ ion.

ii.

Explain why the atomic radius of calcium (atomic number 20) is larger than the atomic radius of titanium (atomic number 22).