Alginate Sphere Uniformity Analyser

Summary Statistics

Descriptive statistics for the batch. The coefficient of variation (CV) is the most useful single measure of uniformity — it expresses the spread relative to the mean and is dimensionless, so different batches can be directly compared.

Mass Distribution

The chart on the left shows each sphere sorted from lightest to heaviest, with mean ± 1 SD shaded. The histogram on the right shows how masses cluster around the mean.

What the spheres actually look like (to scale)

Sorted lightest to heaviest. Calcium alginate hydrogels are ~98% water, so we assume density ≈ 1.02 g/mL to convert mass to volume, then to radius assuming spherical geometry.

Each circle represents one sphere, rendered at approximately true size (1 mm ≈ 4 px). Spread should be visually subtle for a uniform batch.

Physical Interpretation

For a sphere: V = m/ρ, r = (3V/4π)^1/3, SA = 4πr², and SA:V = 3/r. The smallest and largest spheres differ in surface-area-to-volume ratio — the key geometric quantity governing diffusion.

Why SA:V matters: Yeast inside an alginate sphere produces CO₂ throughout the volume. For that CO₂ to lower the buffer pH, it must diffuse out through the sphere's surface. A higher SA:V ratio means more surface area per unit of CO₂-generating volume — i.e. faster equilibration with the surrounding buffer. Smaller spheres release CO₂ to the buffer faster per gram of yeast.

Implications for the 8-sphere Experiment

Your experimental design uses 8 spheres per condition at 0, 20, 40 and 60 °C in 0.01 M bicarbonate buffer (pH 8.3) for 45 min. We need to ask: given the variation in individual sphere mass, how much variation should we expect between conditions purely from sampling, before any biology even happens?

Pooling reduces variation

When 8 spheres are pooled into a single condition, the relative variation in total mass shrinks by a factor of √8 ≈ 2.83 (assuming spheres are picked independently). This is the central limit theorem at work.

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Individual sphere CV

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8-sphere total CV (predicted)

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Expected total mass × 8 (mg)

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95% range, 8-sphere total (mg)

Simulated random draws of 8 spheres (sampled with replacement from your 20), repeated 2000 times:

Surface area to volume and temperature

Two physical processes drive the pH change in this experiment, and they respond differently to temperature:

Temperature	Yeast metabolic rate (Q₁₀ ≈ 2)	CO₂ diffusion coefficient (in water)	Likely outcome
0 °C	≈ 0.25× the 20 °C rate	≈ 0.52× the 20 °C value	Very little CO₂ produced; minimal pH change.
20 °C	baseline (1×)	baseline (1×)	Moderate, measurable pH drop.
40 °C	≈ 4× the 20 °C rate	≈ 1.6× the 20 °C value	Largest pH drop — typically the optimum for S. cerevisiae.
60 °C	brief activity, then thermal death (>55 °C)	≈ 2.4× the 20 °C value	Small early pH change, then plateaus as yeast die.

Crucial framing: the treatment effect of temperature on respiration rate spans roughly a 16-fold range from 0 °C to 40 °C (Q₁₀ = 2), whereas the variation in 8-sphere total mass typically contributes only a small percentage error. So mass uniformity is a minor source of variation compared with the deliberate manipulation — provided the CV is in the few-percent range. If your individual sphere CV exceeds ~10%, this assumption breaks down, particularly at 0 °C where the signal is small.

Where SA:V actually shows up in the data

Imagine two scenarios for how CO₂ release rate depends on sphere geometry:

Volume-limited (reaction-limited): CO₂ release rate is proportional to the total mass of yeast. Doubling sphere volume doubles CO₂ output. In this case, only the total mass of the 8 spheres matters — SA:V is irrelevant. This is likely the dominant regime here, because the alginate gel is permeable to small molecules and the spheres are small (~4–5 mm).
Surface-limited (diffusion-limited): CO₂ release rate is proportional to total surface area. Here a batch of many small spheres would outperform a batch of fewer large spheres with the same total mass. This regime would be more obvious with much larger spheres or denser gels.

For most VCE practicals with these spheres, scenario 1 dominates and mass uniformity is the relevant metric. Scenario 2 is worth discussing with students as a way to motivate why SA:V appears so often in biology.

Alginate Sphere Uniformity Analyser

Step 1: Enter sphere masses

Saved batches

Summary Statistics

Mass Distribution

What the spheres actually look like (to scale)

Physical Interpretation

Implications for the 8-sphere Experiment

Pooling reduces variation

Surface area to volume and temperature

Where SA:V actually shows up in the data