AP Chemistry FRQ Practice

🧪AP Chemistry

Guided Practice

Practice FRQ 1 of 351/35

2. Answer the following questions about zirconium.

A sample of pure zirconium is analyzed using a mass spectrometer. The resulting mass spectrum is shown in Figure 1.

Figure 1. Mass spectrum of zirconium (relative abundances of isotopes)

Create a clean, black-and-white mass spectrum (stick spectrum) with one panel.

Overall layout:
- White background, no gridlines.
- A rectangular plotting region occupying most of the figure, with axes drawn as solid black lines.
- Arrows on the positive ends of both axes.

X-axis (horizontal):
- Axis label centered below the axis: "Mass-to-charge ratio (m/z)".
- Numeric range shown from 89 to 97.
- Tick marks at every 1 m/z unit, labeled with the integers 89, 90, 91, 92, 93, 94, 95, 96, 97.
- The tick labels must be directly under their tick marks and evenly spaced.

Y-axis (vertical):
- Axis label rotated vertically along the left side: "Relative Abundance (%)".
- Numeric range shown from 0 to 60.
- Tick marks every 10%, labeled 0, 10, 20, 30, 40, 50, 60.
- The origin label "0" must appear at the bottom-left intersection of the axes.

Spectrum bars (five vertical lines/bars):
- Exactly five thin vertical black bars (uniform thickness) located exactly above the x-axis tick marks for m/z values 90, 91, 92, 94, and 96 only.
- No bar at 89, 93, 95, or 97.
- Each bar must start exactly at the x-axis baseline (0% line) and extend straight upward to its specified height.
- Bar heights (top of bar aligns exactly with these y-values):
- At m/z 90: height exactly 51.5% (top located slightly above the 50% tick by one and a half percent of the full 0–100% scale, i.e., clearly above 50% but clearly below 60%).
- At m/z 91: height exactly 11.2% (top slightly above the 10% tick and far below the 20% tick).
- At m/z 92: height exactly 17.1% (top clearly below 20% but above 10%, closer to 20% than to 10%).
- At m/z 94: height exactly 17.4% (top clearly below 20% but above 10%, very slightly higher than the 17.1% bar at m/z 92).
- At m/z 96: height exactly 2.8% (top clearly above 0% but well below the 10% tick).

Relative height constraints (must be visually obvious):
- The tallest bar is at m/z 90.
- The second-tallest bar is at m/z 94.
- The third-tallest bar is at m/z 92, and it is almost the same height as the bar at m/z 94 but visibly shorter.
- The fourth-tallest bar is at m/z 91.
- The shortest bar is at m/z 96.

No extra text:
- Do NOT print the percentages above the bars.
- Do NOT add isotope symbols (e.g., 90Zr) on the plot.
- Only the axes, tick labels, and the five bars appear.

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

ii. Explain the difference in atomic structure between the isotope zirconium-90 and the isotope zirconium-91.

In a separate experiment, a 1.500 g sample of pure zirconium metal is heated in an excess of chlorine gas, Cl₂, to form 3.832 g of a solid compound.

i. Calculate the number of moles of chlorine in the 3.832 g sample of the compound produced.

ii. Determine the empirical formula of the compound.

Zirconium is a transition metal with atomic number 40.

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

ii. When zirconium reacts to form the Zr⁴⁺ ion, electrons are removed. Write the complete ground-state electron configuration for the Zr⁴⁺ ion.

The first ionization energies for zirconium and several other Period 5 elements are plotted in the graph in Figure 2.

Figure 2. First ionization energies of selected Period 5 elements

Create a single-panel Cartesian graph on a white background showing first ionization energy versus atomic number for six Period 5 elements.

Overall layout:
- White background, no gridlines.
- A rectangular plotting region with solid black axes.
- Arrows on the positive ends of both axes.

X-axis (horizontal):
- Label centered below the axis: "Atomic Number".
- Numeric range shown from 37 to 42.
- Tick marks at every 1 atomic number unit.
- Every tick is labeled with the integers 37, 38, 39, 40, 41, 42.

Y-axis (vertical):
- Label rotated vertically along the left side: "First Ionization Energy (kJ/mol)".
- Numeric range shown from 300 to 800.
- Tick marks every 50 kJ/mol.
- Tick labels shown at 300, 350, 400, 450, 500, 550, 600, 650, 700, 750, 800.

Origin/axis intersection labeling requirement:
- Because the x-range and y-range do not include zero, do not force a "0" label at the axis intersection.
- Instead, ensure the lowest labeled ticks visible are 37 on the x-axis and 300 on the y-axis, located at the left and bottom edges respectively.

Data markers (exactly six points):
- Plot six filled circular markers (solid black dots), all the same size.
- Each marker is positioned directly above its atomic-number tick and at the exact y-value listed below.
- Next to each marker, place the element symbol (two-letter where applicable) as plain text slightly above and slightly to the right of the dot so the label does not overlap the marker.

Exact values that must be encoded by marker height:
- At atomic number 37: marker at 403 kJ/mol, labeled "Rb".
- At atomic number 38: marker at 549 kJ/mol, labeled "Sr".
- At atomic number 39: marker at 600 kJ/mol, labeled "Y".
- At atomic number 40: marker at 640 kJ/mol, labeled "Zr".
- At atomic number 41: marker at 652 kJ/mol, labeled "Nb".
- At atomic number 42: marker at 684 kJ/mol, labeled "Mo".

Curve/connection rules (must remove ambiguity):
- Do NOT connect the points with a line or curve. This is a scatter plot only.
- No best-fit line.

Curve-shape description (explicitly state none):
- There is no continuous curve. The visual trend is conveyed solely by the rising vertical positions of the six discrete markers from left to right.

Relative vertical ordering constraints (must be visually true):
- The lowest point is Rb (403).
- The next higher point is Sr (549).
- Y (600) is higher than Sr.
- Zr (640) is higher than Y.
- Nb (652) is slightly higher than Zr (only a small vertical gap compared with the 50 kJ/mol tick spacing).
- Mo (684) is the highest point.

No extra annotations:
- No title inside the plotting area.
- No legend box (each point is labeled directly).

i. Using the data in Figure 2 and principles of atomic structure, explain why the first ionization energy of zirconium (Z=40) is greater than the first ionization energy of yttrium (Z=39).

ii. Predict whether the atomic radius of zirconium is greater than, less than, or equal to the atomic radius of yttrium. Justify your prediction.

A student is given a 10.0 g sample of a mixture containing solid ZrO₂ (molar mass 123.22 g/mol) and an inert impurity.

i. Calculate the mass of zirconium (molar mass 91.22 g/mol) in 1.00 mole of pure ZrO₂.

ii. The student analyzes the mixture and determines that it contains 5.50 g of Zr. Calculate the percent by mass of ZrO₂ in the original 10.0 g mixture.