Lab 3 Sample Report

Introduction

This experiment investigated the change in acidity of light roast and dark roast coffee over a 60-minute period. pH was measured at five-minute intervals for each sample to characterize the rate at which each roast generates hydronium ions and to evaluate how roast level affects overall acidity.

Methods

Two coffee samples — one light roast and one dark roast — were prepared using tap water (pH 6.0). pH was recorded every five minutes over 60 minutes using a calibrated pH meter. The resulting concentrations of hydronium ions (\([\text{H}^+]\)) were computed from the measured pH values, and an average rate of acid generation was estimated for each sample.

Results

Figure 1. pH of light roast and dark roast coffee measured at five-minute intervals over 60 minutes.

Salient Features

Light Roast

• Initial pH (t = 0 min): 4.5
• Final pH (t = 60 min): 3.5
• Transition period: The pH was relatively stable near 4.5–5.0 for the first 40 minutes, then declined sharply, reaching its minimum of 3.5 at t = 45 min and remaining there through t = 60 min.

Dark Roast

• Initial pH (t = 0 min): 6.0
• Final pH (t = 60 min): 5.0
• Transition period: The dark roast dropped rapidly from pH 6.0 to 5.0 within the first 15 minutes, then stabilized near pH 5.0 for the remainder of the observation period, with only a brief, minor deviation at t = 25 min (pH 5.5).

Analysis

Hydronium Ion Concentrations

Because

\[ \text{pH} = -\log[\text{H}^+], \]

the corresponding hydronium ion concentrations are:

Light roast: \[ [\text{H}^+]_{0} = 10^{-4.5} = 3.16 \times 10^{-5}\ \text{M} \qquad \rightarrow \qquad [\text{H}^+]_{45} = 10^{-3.5} = 3.16 \times 10^{-4}\ \text{M} \]

Dark roast: \[ [\text{H}^+]_{0} = 10^{-6.0} = 1.00 \times 10^{-6}\ \text{M} \qquad \rightarrow \qquad [\text{H}^+]_{15} = 10^{-5.0} = 1.00 \times 10^{-5}\ \text{M} \]

Each sample reached its minimum pH (maximum acidity) and plateaued: the light roast at t = 45 min and the dark roast at t = 15 min. These endpoints were therefore used as \(\Delta t\) in subsequent rate calculations.

Estimated Rate of Acid Generation

The average rate of hydronium ion production was approximated as

\[ \text{rate} \approx \frac{\Delta[\text{H}^+]}{\Delta t} \]

where \(\Delta t\) spans only the active transition period (from initial measurement to plateau).

Light roast (\(\Delta t = 45\ \text{min}\)): \[ \text{rate} \approx \frac{3.16 \times 10^{-4} - 3.16 \times 10^{-5}}{45\ \text{min}} = \frac{2.84 \times 10^{-4}}{45} \approx 6.3 \times 10^{-6}\ \text{M/min} \]

Dark roast (\(\Delta t = 15\ \text{min}\)): \[ \text{rate} \approx \frac{1.00 \times 10^{-5} - 1.00 \times 10^{-6}}{15\ \text{min}} = \frac{9.00 \times 10^{-6}}{15} = 6.0 \times 10^{-7}\ \text{M/min} \]

The light roast therefore generated hydronium ions at a rate approximately ten times greater than the dark roast during its transition period.

Projected Concentration at 3 Hours

Assuming the estimated rates remain constant, a simple linear model

\[ [\text{H}^+]_t = [\text{H}^+]_0 + (\text{rate}) \cdot t \]

was used to project concentrations at \(t = 180\ \text{min}\):

Light roast: \[ [\text{H}^+]_{180} = 3.16 \times 10^{-5} + (6.3 \times 10^{-6})(180) = 3.16 \times 10^{-5} + 1.13 \times 10^{-3} \approx 1.17 \times 10^{-3}\ \text{M} \quad \Rightarrow \quad \text{pH} \approx 2.93 \]

Dark roast: \[ [\text{H}^+]_{180} = 1.00 \times 10^{-6} + (6.0 \times 10^{-7})(180) = 1.00 \times 10^{-6} + 1.08 \times 10^{-4} \approx 1.09 \times 10^{-4}\ \text{M} \quad \Rightarrow \quad \text{pH} \approx 3.96 \]

These projections should be interpreted with caution. Both samples appeared to plateau well before 60 minutes, suggesting that the system is approaching chemical equilibrium. A constant-rate model does not account for this equilibration, and actual concentrations at 180 minutes would likely be considerably lower than projected.

Conclusion

Both coffee samples became more acidic over the observation period, consistent with the ongoing hydrolysis and oxidation of organic acids during brewing and exposure to air. The light roast was substantially more acidic than the dark roast throughout the experiment, both in absolute pH and in rate of acid generation — consistent with the well-established finding that darker roasting degrades a greater proportion of chlorogenic and other organic acids. The dark roast reached its apparent equilibrium pH much more quickly (≈15 min) than the light roast (≈45 min), suggesting a lower overall buffering capacity or a smaller quantity of reactive acid precursors.

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Appendix: Raw Data

Table A1. pH measurements of light roast and dark roast coffee over 60 minutes. Tap water pH: 6.0.

Time Elapsed (min)	Light Roast pH	Dark Roast pH
0	4.5	6.0
5	5.0	6.0
10	5.0	6.0
15	5.0	5.0
20	5.0	5.0
25	5.0	5.5
30	4.5	5.0
35	5.0	5.0
40	4.5	5.0
45	3.5	5.0
50	4.0	5.0
55	3.5	5.0
60	3.5	5.0