AP Chemistry FRQ Practice

Practice FRQ 1 of 13

1. Answer the following questions about the element gallium, Ga.

The mass spectrum for a sample of gallium is shown in Figure 1. The sample contains two stable isotopes, gallium-69 and gallium-71.

Figure 1. Mass spectrum of gallium isotopes

Single-panel vertical bar chart (mass spectrum).

Canvas/layout:
- White background, no gridlines.
- Plotting rectangle corners: left edge at x=0.10W, right edge at x=0.95W, bottom edge at y=0.15H, top edge at y=0.90H (W = total image width, H = total image height).

Axes:
- Horizontal axis along the bottom of the plotting rectangle.
- Axis label centered below axis: "Mass Number" (no units).
- Numeric axis range: 68 to 72 inclusive.
- Major tick marks at exactly 68, 69, 70, 71, 72 (tick interval = 1 mass unit).
- Each tick label printed directly below its tick.
- Vertical axis along the left of the plotting rectangle.
- Axis label centered left of axis, rotated 90°: "Relative Abundance (%)".
- Numeric axis range: 0 to 100.
- Major tick marks at exactly 0, 20, 40, 60, 80, 100 (tick interval = 20%).
- Tick labels printed left of the axis.
- Both axes end with arrowheads at the positive ends (right end of x-axis and top end of y-axis).

Bars (two total):
- Bars are solid black rectangles with sharp corners, no outlines beyond fill.
- Baseline of both bars is exactly at y = 0% (touching the x-axis line).
- Bar centers align exactly with mass numbers 69 and 71.
- Bar width: exactly 0.60 mass-number units for each bar.
- Therefore, the left and right x-edges are:
- For mass 69 bar: x = 68.70 to x = 69.30.
- For mass 71 bar: x = 70.70 to x = 71.30.
- Bar heights (top edges) must align exactly with the following y-values on the y-axis scale:
- At mass number 69: top edge at y = 60.1%.
- At mass number 71: top edge at y = 39.9%.

Numeric annotations (to force exact values):
- Place text "60.1%" centered horizontally above the 69 bar, with the bottom of the text 2% (i.e., 2 units on the y-scale) above the bar top (text baseline at y=62.1%).
- Place text "39.9%" centered horizontally above the 71 bar, with the bottom of the text 2% above the bar top (text baseline at y=41.9%).

Isotope identifiers (explicit for Part A(ii)):
- Directly below the x-axis, centered under tick 69, add label "Ga-69".
- Directly below the x-axis, centered under tick 71, add label "Ga-71".
- Add a small note inside the plotting area near the 69 bar (upper right of that bar, not overlapping): "most abundant".

No additional bars, curves, or legend.

i. Using the data in Figure 1, calculate the average atomic mass of gallium.

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

Figure 2. Mass data for gallium oxide formation

A 2-column, 4-row table (1 header row + 3 data rows). No merged cells.

Table structure:
- Column 1 header (top-left cell): "Measurement".
- Column 2 header (top-right cell): "Mass (g)".

Rows (exact text in each cell):
- Row 1 (header): Measurement | Mass (g)
- Row 2: Mass of empty crucible | 25.000
- Row 3: Mass of crucible + gallium | 26.394
- Row 4: Mass of crucible + gallium oxide | 26.874

Formatting constraints to enforce readability:
- All masses displayed with exactly three digits after the decimal.
- Right-align the numeric entries in the "Mass (g)" column.
- Left-align the text in the "Measurement" column.
- Use thin black cell borders for all internal and external lines.

B. A student investigates the reaction of gallium with oxygen to determine the empirical formula of a gallium oxide compound. The student heats a sample of gallium in a crucible, allowing it to react with atmospheric oxygen. The data collected is shown in Figure 2.

i. Using the data in Figure 2, calculate the number of moles of gallium that reacted. (The molar mass of gallium is 69.72 g/mol).

ii. Calculate the number of moles of oxygen that reacted.

C. Using your answers from part B, determine the empirical formula of the gallium oxide.

The properties of gallium are determined by its atomic structure.

D. Explain why the atomic radius of a gallium atom (135 pm) is smaller than the atomic radius of a calcium atom (197 pm). Justify your answer using Coulomb's law and the principles of atomic structure.

Figure 3. Photoelectron spectrum of gallium valence region

Single-panel photoelectron spectrum (line plot with three peaks) on a reversed binding-energy x-axis.

Canvas/layout:
- White background, no gridlines.
- Plotting rectangle corners: left edge at x=0.12W, right edge at x=0.95W, bottom edge at y=0.15H, top edge at y=0.90H.

Axes:
- Horizontal axis along the bottom of the plotting rectangle.
- Axis label centered below axis: "Binding Energy (MJ/mol)".
- Reversed numeric axis: leftmost tick is 5.00 and rightmost tick is 0.00.
- Major ticks at exactly: 5.00, 4.00, 3.00, 2.00, 1.00, 0.00 (tick interval = 1.00 MJ/mol).
- The numeric labels decrease from left to right.
- Vertical axis along the left side of the plotting rectangle.
- Axis label rotated 90°: "Relative Intensity (arbitrary units)".
- Numeric range: 0 to 10.
- Major ticks at exactly 0, 2, 4, 6, 8, 10 (tick interval = 2 units).
- Axes drawn in solid black with arrowheads at positive ends (rightward arrow on x-axis direction is visually to the right even though values decrease; upward arrow on y-axis).

Spectrum baseline and line style:
- Baseline is exactly y = 0 from x = 5.00 to x = 0.00.
- Spectrum drawn as a single continuous solid black curve (2 pt thickness), sitting on the baseline except where peaks occur.

Peak definitions (three symmetric triangular peaks to force exact apex positions and heights):
- Peak A (leftmost peak):
- Apex exactly at (x = 2.90 MJ/mol, y = 10.0).
- Left base point exactly at (x = 3.20, y = 0.0).
- Right base point exactly at (x = 2.60, y = 0.0).
- Connect left base to apex with a straight line; connect apex to right base with a straight line.
- Peak B (middle peak):
- Apex exactly at (x = 1.30 MJ/mol, y = 2.0).
- Left base point exactly at (x = 1.50, y = 0.0).
- Right base point exactly at (x = 1.10, y = 0.0).
- Straight-line sides.
- Peak C (rightmost peak):
- Apex exactly at (x = 0.59 MJ/mol, y = 1.0).
- Left base point exactly at (x = 0.69, y = 0.0).
- Right base point exactly at (x = 0.49, y = 0.0).
- Straight-line sides.

Peak labels and numeric annotations (to prevent x-location drift):
- Place label "A" 0.05 MJ/mol to the left of Peak A apex and at y = 9.5 (text anchor at x=2.85, y=9.5).
- Place label "B" 0.05 MJ/mol to the left of Peak B apex and at y = 1.7 (x=1.25, y=1.7).
- Place label "C" 0.05 MJ/mol to the left of Peak C apex and at y = 0.8 (x=0.54, y=0.8).
- Directly above each apex, print the binding energy value centered on the apex x-position:
- Above Peak A apex: "2.90 MJ/mol" at y = 10.3.
- Above Peak B apex: "1.30 MJ/mol" at y = 2.3.
- Above Peak C apex: "0.59 MJ/mol" at y = 1.3.

Subshell callout for Part E(i):
- Add a leader line (thin black) from text "4p" to Peak C apex at (0.59, 1.0). The text "4p" is placed at (x = 0.90, y = 3.0), and the leader line ends exactly at the apex of Peak C.

No additional peaks or legend.

E. The photoelectron spectrum for the valence shell of gallium is shown in Figure 3.

i. Identify the subshell corresponding to the peak at 0.59 MJ/mol in Figure 3.

ii. A peak for the 3d subshell of zinc (Zn, Z=30) would appear at a different binding energy than the 3d peak for gallium shown in Figure 3. Predict whether the binding energy for the Zn 3d peak would be greater than, less than, or equal to the binding energy of the Ga 3d peak. Explain.

F. In the experiment described in part B, the student did not heat the crucible long enough to completely drive off all atmospheric moisture before weighing the final product. Would the calculated mass percent of oxygen in the gallium oxide be greater than, less than, or equal to the actual mass percent of oxygen? Justify your answer.