Question

Correcting previous help question again. How do I use the formula Rate[mm/h]=(diameter [mm]/time [min]) x 60 [min] to help evaluate my hypothesis: The greater the concentration gradient, the faster the diffusion rate. Here is my data: Time (min) 1 crystal 5 min 10mm 10 min 15mm 15 min 20mm 2 crystals 5 min 15mm 10 min 20mm 15 min 25mm 4 crystals 5 min 20mm 10 min 25mm 15 min 30mm.
How do I find average diff speed at 0-5 0-10 0-15 for 1 crystal, 2 crystals, and 4 crystals? Then I must graph with I believe a bar graph works best.

Accepted Answer

Utilizing this equation depends on whether you want to analyze the rate for selected portions of your experiment time or the entire duration of the experiment. This is important, because your rate is changing, and if you average it out, your averages may not reflect the actual rate per hour.
All three of your samples appear to show a significant change in their rate, with a linear growth rate after 5 minutes but a significantly higher rate prior to that. For example, your 1 crystal sample, assuming it starts at a diameter of 0, shows a growth of 11mm in 5 minutes. Projecting this over the course of one hour, you would multiply both values by 12, to get 132mm per 60 minutes (a rate of 132mm/h). However if we use the next time interval, where the crystal only grows 4mm in 5 minutes, this provides a rate of 48mm/h, which is significantly less. If we look at the total growth over 15 minutes, we get 80mm/h, which is also significantly different.
I'm assuming that the number of crystals in your data refers to the concentration gradient. If you ignore the linear growth shown after 5 minutes in all three samples, then yes, it appears your hypothesis is confirmed, because the initial growth rate (from 0 to 5 min) increases in direct proportion to the number of crystals:
1 crystal: 11mm/5min = 132mm/h
2 crystals: 15mm/5min = 180mm/h
4 crystals: 20mm/5min = 240mm/h
After 5 minutes, all of your crystals show the same rate of growth. I would recommend a line graph in order to show the different initial rates relative to each other (with increasingly steep slopes reflecting confirmation of the hypothesis) with a 1:1 linear increase thereafter. You could then show the rates during the initial 5 minutes as a separate bar graph to emphasize that the hypothesis was correct.
If you want to calculate rates for any given time interval, you simply need to divide 60 by the length of the time interval. Take that result and multiply it by the growth during that time interval in order to find the rate per hour.

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