Quantitative Analysis Using Smartphone Colorimetry - Interactive Edition
Spectroscopy is the study of how matter interacts with light. When light passes through a colored solution, some wavelengths are absorbed while others pass through (are transmitted). The color we see is the light that is NOT absorbed.
For example, grape juice appears purple/violet because it absorbs light in the yellow-green region of the spectrum and transmits (reflects) red and blue wavelengths, which combine to create the purple color we perceive.
Beer's Law describes the relationship between the concentration of a solution and the amount of light it absorbs:
When light enters a sample, we measure what comes out the other side:
Grape juice absorbs GREEN light most strongly. By using green construction paper as our background light source, we maximize the signal change as concentration increases. The app will measure the green channel intensity - as grape juice concentration increases, less green light passes through, and the green channel reading decreases.
Complete these questions before coming to lab:
Write Beer's Law equation and define each variable:
If light intensity through a blank (\(I_0\)) is 200 and through a sample (\(I\)) is 100, calculate:
a) Transmittance (\(T = I/I_0\))
b) Absorbance (\(A = -\log_{10} T\))
Show your calculations:
Grape juice appears purple/violet. Based on the color wheel, what color light does it primarily absorb? Why are we using green construction paper as our background?
Which RGB channel (Red, Green, or Blue) should show the greatest change in intensity as grape juice concentration increases? Explain your reasoning.
Name TWO real-world applications where colorimetry/spectroscopy is used:
Download this app before coming to lab:
Carolina RGB Colorimeter (iOS)
This app displays real-time RGB values from your phone's camera, allowing us to measure light intensity passing through our samples.
Follow these steps to construct your colorimeter. Consistency in construction is essential for accurate measurements.
ROOM LIGHT
|
v
+------------------+
| | GREEN CONSTRUCTION
| [OPEN BACK] <---- PAPER (light source)
| |
| [CUVETTE] | Sample position
| | | (mark this spot!)
| v |
| [FRONT HOLE] ------> PHONE CAMERA
| | (RGB app)
+------------------+
Light reflects off green paper, passes through
sample, exits front hole to phone camera.
Sketch your colorimeter setup and label: Front viewing hole, Sample/cuvette position, Green construction paper, Phone placement, Light path (arrows)
You will prepare 6 standard solutions by diluting the grape juice stock (100%) with distilled water. Each solution should have a total volume of 10 mL.
| Standard | Concentration (%) | Grape Juice (mL) | Distilled Water (mL) | Total Volume (mL) |
|---|---|---|---|---|
| Blank | 0% | 0 | 10 | 10 |
| Std 1 | 20% | 2 | 8 | 10 |
| Std 2 | 40% | 4 | 6 | 10 |
| Std 3 | 60% | 6 | 4 | 10 |
| Std 4 | 80% | 8 | 2 | 10 |
| Std 5 | 100% | 10 | 0 | 10 |
Verify Standard 2 (40% grape juice):
\(C_1\) (stock concentration) = %
\(V_1\) (volume of stock) = mL
\(C_2\) (desired concentration) = %
\(V_2\) (total final volume) = mL
Verification:
Channel: GREEN
\(I_0\) =
Enter your intensity readings. Transmittance (T) and Absorbance (A) will calculate automatically.
| Sample | Conc. (%) | \(I\) (Reading 1) | \(I\) (Reading 2) | \(I\) (Average) | \(T = I/I_0\) | \(A = -\log(T)\) |
|---|---|---|---|---|---|---|
| Blank | 0 | \(I_0\) (entered above) | 1.000 | 0.000 | ||
| Std 1 | 20 | -- | -- | -- | ||
| Std 2 | 40 | -- | -- | -- | ||
| Std 3 | 60 | -- | -- | -- | ||
| Std 4 | 80 | -- | -- | -- | ||
| Std 5 | 100 | -- | -- | -- | ||
| Unknown | ? | -- | -- | -- | ||
Calculate \(T\) and \(A\) for Standard 3 using your recorded values:
Your calibration curve plots Absorbance (A) vs. Concentration (%). The graph updates in real-time as you enter data.
Using the equation \(A = m \cdot C + b\), solve for \(C\):
Your unknown absorbance: --
Calculated unknown concentration:
Unknown Grape Juice Concentration:
Enter your final answer below:
Discuss TWO potential sources of error in this experiment (besides auto-exposure on your phone camera). For each error, explain how it could impact your calibration curve's linearity or accuracy.
Error 1:
Error 2:
Clinical Application: In a hospital, Beer's Law is used in pulse oximetry to measure blood oxygen saturation. If a patient has jaundice (high bilirubin, which absorbs blue light), how might this interfere with the oximeter's red/infrared readings? What could clinicians do to address this interference?
Your calibration curve should ideally pass through the origin (0,0). Did yours? If it had a y-intercept significantly different from zero, what might have caused this?
Beer's Law states that absorbance is directly proportional to concentration. What would you expect to happen to this linear relationship if you tested very high concentrations (beyond 100% of what we used)? Explain why Beer's Law might "fail" at high concentrations.
If you wanted to measure the concentration of a YELLOW solution instead of grape juice:
a) What color construction paper would you use?
b) Which RGB channel would you measure?
c) Explain your reasoning:
A classmate got a negative absorbance value for one of their samples. What likely went wrong, and how should they troubleshoot this issue?
Student: --
Date: --
Section: --
\(I_0\) (Blank): --
\(R^2\): --
Unknown Concentration: -- %
Prepare unknowns at concentrations that fall within the calibration range but are NOT identical to any standard:
Preparation for 50 mL of 35% unknown:
17.5 mL grape juice + 32.5 mL water = 50 mL at 35%
| Component | Points | Criteria |
|---|---|---|
| Pre-lab Questions | 15 | Complete and correct answers showing understanding |
| Data Collection | 25 | Complete data table, reasonable values, proper calculations |
| Calibration Curve | 20 | Correct axes, linear trend, \(R^2 > 0.95\) |
| Unknown Determination | 15 | Correct method, within +/- 10% of actual value |
| Post-lab Questions | 20 | Thoughtful, complete answers demonstrating understanding |
| Lab Technique | 5 | Safety, cleanliness, proper procedure |
| Total | 100 |
| Sample | Conc. (%) | \(I\) (Avg) | \(T\) | \(A\) |
|---|---|---|---|---|
| Blank | 0 | 185 | 1.000 | 0.000 |
| Std 1 | 20 | 152 | 0.822 | 0.085 |
| Std 2 | 40 | 124 | 0.670 | 0.174 |
| Std 3 | 60 | 98 | 0.530 | 0.276 |
| Std 4 | 80 | 76 | 0.411 | 0.386 |
| Std 5 | 100 | 58 | 0.314 | 0.503 |
| Unknown | ~55% | 105 | 0.568 | 0.246 |
Equation: \(A = 0.005 \cdot C\)
\(R^2\): 0.998
Given: \(A_{\text{unknown}} = 0.246\)
Using: \(C = \frac{A - b}{m}\)
\(C = \frac{0.246 - 0.0032}{0.00497}\)
\(C = \frac{0.2428}{0.00497}\)
\(C = 48.9\%\) (approximately 49%)
If actual unknown was 55%: percent error = \(\frac{|49-55|}{55} \times 100 = 10.9\%\)
\(A = \varepsilon \cdot l \cdot c\)
\(A\) = absorbance (unitless)
\(\varepsilon\) = molar absorptivity (L·mol⁻¹·cm⁻¹)
\(l\) = path length (cm)
\(c\) = concentration (mol/L or %)
a) \(T = I/I_0 = 100/200 = 0.50\)
b) \(A = -\log_{10}(0.50) = -(-0.301) = 0.301\)
Grape juice absorbs primarily GREEN/YELLOW light (complementary to purple/violet). We use green construction paper because it provides green light that will be absorbed by the grape juice. The more concentrated the grape juice, the more green light is absorbed, giving us a measurable signal change.
The GREEN channel should show the greatest change. Since grape juice absorbs green light, as concentration increases, less green light passes through. The green channel reading will decrease from high (blank) to low (100% grape juice).
Accept any two valid applications:
Accept any two valid errors with explanations:
Jaundice (bilirubin) absorbs blue light, which could interfere with the pulse oximeter's measurements. The additional light absorption might be misinterpreted as deoxygenated hemoglobin, potentially causing falsely low SpO2 readings. Clinicians can: (1) use co-oximetry which measures at more wavelengths, (2) draw arterial blood gas for direct measurement, (3) apply correction factors if bilirubin levels are known, or (4) use newer devices with additional wavelengths designed to account for interfering substances.
Ideally the curve passes through origin (0,0) because zero concentration should give zero absorbance. A non-zero y-intercept could be caused by: (1) stray light in the colorimeter, (2) blank solution contamination, (3) light leaks in the box, (4) reflection/scattering from cuvette walls, or (5) systematic measurement error in all readings.
At very high concentrations, Beer's Law deviates from linearity and the calibration curve would level off (plateau). This occurs because: (1) molecules interact with each other at high concentrations, changing their absorption properties, (2) solute-solute interactions alter the local environment, (3) refractive index changes significantly, and (4) the solution may become saturated. This is called "positive deviation" from Beer's Law.
a) Blue or violet construction paper (complementary color to yellow)
b) Blue channel
c) Yellow solutions absorb blue/violet light. Using blue paper as the background provides blue light that will be absorbed by the yellow solution. The blue channel reading will decrease as yellow solution concentration increases, giving us the greatest dynamic range for measurement.
Negative absorbance means \(I > I_0\) (sample reading higher than blank). Possible causes: (1) blank was measured incorrectly or at a different time when lighting was different, (2) auto-exposure adjusted between measurements, (3) sample cuvette was cleaner than blank cuvette, (4) sample position was different (closer to light source), (5) blank solution was accidentally contaminated. To troubleshoot: re-measure blank and sample immediately after each other, verify exposure is locked, check cuvette cleanliness, mark exact sample position.
\(C_1 = 100\%\), \(V_1 = 4\) mL, \(C_2 = 40\%\), \(V_2 = 10\) mL
Verification: \(100 \times 4 = 40 \times 10 = 400\)