Fermentation of glucose I have trouble understanding as to what the last part of the increase in liquid level means. I believe this is the foam formed after the fermentation? I am calculating for the pressure but I have trouble as to what volume should I use to find the moles since I don't understand the last part. It would greatly help me to understand this process first.
I've been extensively searching how the fermentation process actually occurs cause I don't understand a thing about it. To find the pressure from what I know, I converted the volume of glucose to $\ce{CO2}$ to find the moles and plugged the value in the ideal gas equation $p=nRT/v$ with the volume being $\pu{0.07L}$ from $(\pu{125mL} - \pu{55mL})$, because it says the $\ce{CO2}$ in solution is negligible.
I don't know where the changes in densities come in and I don't know how to incorporate the pressure brought about by the liquid solution. I think my thought process is wrong really cause I don't understand fermentation.
https://www.homebrewtalk.com/threads/calculating-total-gas-produced-in-fermentation.165020/ This site proposed a $p_1v_1=p_2v_2$ method where $p_1$ is at STP, but I don't think this is needed in the problem.
It seems to me like the task description is wrong, like if they maybe do not consider the decrease of mass of the liquid. As the volume increase due lower density is well compensated by the mass decrease.
If I do not count with decrease of the solution mass, I can get the final volume $\pu{55 mL}$.
Note the $x$ is the glucose conversion factor. $x-0$ means glucose only, $x=1$ means ethanol only.
&quot;V wrong&quot; means the volume change, that is accounting with density decrease due glucose -&gt; ethanol conversions, but not accounting with mass decrease of the liquid.
$\ce{CO2}$ calculations are done by Mathew, no need to doubling that.
$\begin{array}{|c|c|c|c|c|c|c|c|c|c|} \hline
\text{x} &amp; \text{H2O[g]} &amp; \text{glu[g]} &amp; \text{eth[g]} &amp;\text{CO2[g]} &amp; \text{liq[g]} &amp; \text{Eth w/w%} &amp; \text{ $\rho$ g/mL} &amp; \text{ V[mL]} &amp; \text{ V[mL] wrong}\\ \hline
0 &amp; 44.0 &amp; 10.00 &amp; 0.00 &amp; 0.00 &amp; 54.00 &amp; 0.00 &amp; 1.080 &amp; 50.00 &amp; 50.00 \\ \hline
0.05 &amp; 44.0 &amp; 9.50 &amp; 0.26 &amp; 0.24 &amp; 53.76 &amp; 0.48 &amp; 1.075 &amp; 50.01 &amp; 50.24 \\ \hline
0.1 &amp; 44.0 &amp; 9.00 &amp; 0.51 &amp; 0.49 &amp; 53.51 &amp; 0.97 &amp; 1.070 &amp; 50.02 &amp; 50.48 \\ \hline
0.15 &amp; 44.0 &amp; 8.50 &amp; 0.77 &amp; 0.73 &amp; 53.27 &amp; 1.46 &amp; 1.065 &amp; 50.04 &amp; 50.72 \\ \hline
0.2 &amp; 44.0 &amp; 8.00 &amp; 1.02 &amp; 0.98 &amp; 53.02 &amp; 1.96 &amp; 1.059 &amp; 50.05 &amp; 50.97 \\ \hline
0.25 &amp; 44.0 &amp; 7.50 &amp; 1.28 &amp; 1.22 &amp; 52.78 &amp; 2.46 &amp; 1.054 &amp; 50.06 &amp; 51.22 \\ \hline
0.3 &amp; 44.0 &amp; 7.00 &amp; 1.53 &amp; 1.47 &amp; 52.53 &amp; 2.96 &amp; 1.049 &amp; 50.07 &amp; 51.47 \\ \hline
0.35 &amp; 44.0 &amp; 6.50 &amp; 1.79 &amp; 1.71 &amp; 52.29 &amp; 3.47 &amp; 1.044 &amp; 50.09 &amp; 51.72 \\ \hline
0.4 &amp; 44.0 &amp; 6.00 &amp; 2.04 &amp; 1.96 &amp; 52.04 &amp; 3.99 &amp; 1.039 &amp; 50.10 &amp; 51.98 \\ \hline
0.45 &amp; 44.0 &amp; 5.50 &amp; 2.30 &amp; 2.20 &amp; 51.80 &amp; 4.51 &amp; 1.034 &amp; 50.11 &amp; 52.24 \\ \hline
0.5 &amp; 44.0 &amp; 5.00 &amp; 2.56 &amp; 2.44 &amp; 51.56 &amp; 5.04 &amp; 1.029 &amp; 50.12 &amp; 52.50 \\ \hline
0.55 &amp; 44.0 &amp; 4.50 &amp; 2.81 &amp; 2.69 &amp; 51.31 &amp; 5.57 &amp; 1.023 &amp; 50.14 &amp; 52.76 \\ \hline
0.6 &amp; 44.0 &amp; 4.00 &amp; 3.07 &amp; 2.93 &amp; 51.07 &amp; 6.10 &amp; 1.018 &amp; 50.15 &amp; 53.03 \\ \hline
0.65 &amp; 44.0 &amp; 3.50 &amp; 3.32 &amp; 3.18 &amp; 50.82 &amp; 6.64 &amp; 1.013 &amp; 50.16 &amp; 53.30 \\ \hline
0.7 &amp; 44.0 &amp; 3.00 &amp; 3.58 &amp; 3.42 &amp; 50.58 &amp; 7.19 &amp; 1.008 &amp; 50.18 &amp; 53.57 \\ \hline
0.75 &amp; 44.0 &amp; 2.50 &amp; 3.83 &amp; 3.67 &amp; 50.33 &amp; 7.74 &amp; 1.003 &amp; 50.19 &amp; 53.85 \\ \hline
0.8 &amp; 44.0 &amp; 2.00 &amp; 4.09 &amp; 3.91 &amp; 50.09 &amp; 8.30 &amp; 0.998 &amp; 50.20 &amp; 54.12 \\ \hline
0.85 &amp; 44.0 &amp; 1.50 &amp; 4.34 &amp; 4.16 &amp; 49.84 &amp; 8.86 &amp; 0.993 &amp; 50.22 &amp; 54.40 \\ \hline
0.9 &amp; 44.0 &amp; 1.00 &amp; 4.60 &amp; 4.40 &amp; 49.60 &amp; 9.43 &amp; 0.987 &amp; 50.23 &amp; 54.69 \\ \hline
0.95 &amp; 44.0 &amp; 0.50 &amp; 4.86 &amp; 4.64 &amp; 49.36 &amp; 10.00 &amp; 0.982 &amp; 50.25 &amp; 54.97 \\ \hline
1 &amp; 44.0 &amp; 0.00 &amp; 5.11 &amp; 4.89 &amp; 49.11 &amp; 10.58 &amp; 0.977 &amp; 50.26 &amp; 55.26 \\ \hline
\end{array}$