Long free-response question

Measuring the Ksp of silver chromate

Units 3 and 7
10 points
About 23 minutes

You can use a calculator on this question, just like on exam day.

A multipart question, often built around a lab setup or a data table, that mixes several topics. You calculate, explain and justify your answers across many lettered parts. On the exam: 3 questions (Questions 1–3), part of the 1-hour-45-minute free-response section; calculator allowed.

The question and its sources

Silver chromate, Ag₂CrO₄, is a slightly soluble red-brown solid. Chromate ions, CrO₄²⁻(aq), strongly absorb near-ultraviolet and violet light, with maximum absorbance at 372 nm; the other ions present do not absorb at this wavelength. A student uses spectrophotometry to determine the Ksp of Ag₂CrO₄ at 25 °C.

Table 1. Calibration data for CrO₄²⁻ at 372 nm (path length 1.00 cm)

[CrO₄²⁻] (M)	Absorbance
2.00 × 10⁻⁵	0.097
4.00 × 10⁻⁵	0.192
6.00 × 10⁻⁵	0.290
8.00 × 10⁻⁵	0.384
1.00 × 10⁻⁴	0.481

Source: Hypothetical data

Saturated solution

The student stirs excess Ag₂CrO₄(s) in distilled water at 25 °C until equilibrium is established, filters the mixture, and measures the absorbance of the clear filtrate in the same 1.00 cm cuvette at 372 nm. The absorbance is 0.313.

Source: Hypothetical data

Suggested time: 23 minutes

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Part (a)

1 point

The standard solutions were prepared from a 1.00 × 10⁻³ M K₂CrO₄ stock solution. Describe how to prepare 50.00 mL of the 4.00 × 10⁻⁵ M standard, including the volume of stock solution needed and the specific glassware you would use.

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Part (b)

1 point

Describe the graph you would construct from the data in Table 1 to use as a calibration curve. Include what is plotted on each axis (with units, if any), the type of plot, and the expected shape of the data.

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Part (c)

1 point

Determine the molar absorptivity, ε, of CrO₄²⁻ at 372 nm. Include units with your answer.

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Part (d)

1 point

Calculate [CrO₄²⁻] in the saturated solution.

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Part (e)

2 points

Write the Ksp expression for Ag₂CrO₄, and calculate the value of Ksp.

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Part (f)

1 point

Calculate the energy, in joules, of one photon of light with a wavelength of 372 nm.

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Part (g)

1 point

Explain why the student set the spectrophotometer to 372 nm rather than to a wavelength such as 600 nm, where CrO₄²⁻ absorbs very little light.

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Part (h)

1 point

Suppose some fine particles of Ag₂CrO₄(s) passed through the filter and were present in the cuvette during the absorbance measurement. Would the calculated value of Ksp be too high, too low, or unaffected? Justify your answer.

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Part (i)

1 point

Calculate the molar solubility of Ag₂CrO₄ in 0.0100 M AgNO₃(aq) at 25 °C. Explain why it differs from the molar solubility in pure water.

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