Lab 3 Sample Report
Data
| 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 |
pH of tap water used: 6
Analysis
Plot of pH against time for light and dark roasts:
The pH of both coffee samples decreased over the 60-minute period, indicating an increase in hydronium ion concentration over time. The light roast decreased from pH 4.5 to 3.5, while the dark roast decreased from pH 6.0 to 5.0. Because
\[ \text{pH} = -\log[H^+], \]
even a change of one pH unit corresponds to a tenfold increase in hydronium ion concentration. Converting the values gives:
Light roast: \[ [H^+]_{0} = 3.16\times10^{-5}\,\text{M} \quad \rightarrow \quad [H^+]_{60} = 3.16\times10^{-4}\,\text{M} \]
Dark roast: \[ [H^+]_{0} = 1.0\times10^{-6}\,\text{M} \quad \rightarrow \quad [H^+]_{60} = 1.0\times10^{-5}\,\text{M} \]
Thus, both samples became more acidic, but the light roast exhibited a much larger absolute increase in \([H^+]\). This trend is consistent with the fact that darker roasting degrades a greater fraction of organic acids, resulting in less bright and acidic taste compared to lighter roasts.
Approximating the reaction rate using
\[ \text{rate} \approx \frac{\Delta[H^+]}{\Delta t}, \]
Light roast: \[ \text{rate} \approx \frac{2.84\times10^{-4}\,\text{M}}{60\,\text{min}} = 4.7\times10^{-6}\,\text{M/min} \]
Dark roast: \[ \text{rate} \approx \frac{9.0\times10^{-6}\,\text{M}}{60\,\text{min}} = 1.5\times10^{-7}\,\text{M/min} \]
The light roast therefore generates hydronium ions at a rate roughly thirty times greater than the dark roast under this linear approximation.
To project the concentration after 3 hours (180 minutes), we assumed this rate remained constant and applied a linear model:
\[ [H^+]_t = [H^+]_0 + (\text{rate})(t) \]
For the light roast:
\[ [H^+]_{180} = 3.16\times10^{-5} + (4.7\times10^{-6})(180) \]
\[ = 3.16\times10^{-5} + 8.46\times10^{-4} \approx 8.8\times10^{-4}\,\text{M} \]
For the dark roast:
\[ [H^+]_{180} = 1.0\times10^{-6} + (1.5\times10^{-7})(180) \]
\[ = 1.0\times10^{-6} + 2.7\times10^{-5} \approx 2.8\times10^{-5}\,\text{M} \]
These projected concentrations were then converted back to pH using
\[ \text{pH} = -\log[H^+], \]
giving approximately pH 3.1 for the light roast and pH 4.6 for the dark roast. This constant-rate assumption is unrealistic, as reaction rates typically decrease as equilibrium is approached. Overall, the light roast demonstrated both a greater total increase in hydronium ion concentration and a significantly higher estimated rate of acid generation during the observation period.