Well, after this came up in another question and after realizing data on this was hard to find online, I pulled out my graduated cylinder and tried it myself. As noted in comments, measuring sugar by volume is very inexact. I found that simply by pouring sugar into the graduated cylinder and tapping it, I could start with about 110mL and tap it down to about 90mL. Even without considering other problems like possible clumps in sugar or the fact that different brands of granulated sugar may have different particle size (and thus different densities), this is already a huge source of potential variation. So, I tried getting a volume of sugar that was about 100mL on average (that is, tapped down to settle slightly, but not completely). Using 100mL of water and adding this volume of sugar gave me a solution of approximately 158mL. That means the combined volume of the dissolved sugar-water mixture was about 79% of the combined volume of the original sugar plus water. Again, I note about a +/-10% variance in sugar density depending on how it is measured, which means the possible range here should be around 76% to 82%, depending on how "settled" the sugar was when I measured it. This is in close agreement with widebandit's post here that found a ratio of 25 fluid oz. solution to 32 fl. oz. of original ingredients, or about 78%, though just a bit higher than Jeff Axelrod's ratio of 75%. Maybe someday I'll try this with a few different brands of sugar, but I just thought I'd add one more datapoint that's close to the other answers here, with some information on how much variance to expect.
Most recent answer: 08/04/2016 When forgetting to turn off heat for boiling sugar water for feeding hummingbirds, does just the water boil off so that I can re-add water to the fill line and still have the correct ratio sugar to water or does some of the sugar boil off too so that what's left is still the correct ratio?- Gail Smith (age 70) Sequim WA USA The sugar does not boil off, so all the sugar you added is still there. Whether you can just add more water to the same line or not depends on how you measured the sugar in the first place. The problem, of course, is that one cup of sugar plus one cup of water does not make two cups of sugar water—the volume will be much less once the sugar and water mix. There are two effects at work here. First, a cup of sugar has a lot of empty space in between the sugar grains, and water can fill up that space (think about adding water to a full cup of sugar; you could add quite a bit before it started to overflow). Second, when the sugar dissolves into individual molecules, the sugar and water molecules can get much closer together, further decreasing the total volume. We know how this works for sugar and water, but predicting exactly what happens when any substance dissolves into another is actually a complicated topic, and chemists are still learning how to model it and understand it. So, if you originally measured the volume of the water with the sugar dissolved in it, you can just add water back to the original volume. If not, it will be much harder to get a predictable result. Here's another option: instead of using volume to figure out how much water to add, you could use weight. You would need a kitchen scale to do this. I assume you know how much sugar you added, either in volume (cups) or weight (grams). If you used volume, convert it to weight: 1 cup of white sugar is about 200 grams. Weigh the remaining solution. You'll have to pour it out of the original container to do this, unless you happen to know the weight of the pot. Since all the sugar is still there, if the solution weighs more than just the sugar, the extra weight is water. You can take that extra water weight, convert it to a volume if you want (1 cup of water is about 225 grams), and figure out how much more water you need to add to reach the desired ratio. Rebecca H. (published on 08/04/2016) Follow-up on this answer
 Hello and thank you for your question on how to calculate the resulting volume when adding powder to liquid. There is no short answer here so let's jump right into the calculations. INTRODUCTION Firstly it is important to understand that when you're looking at the chemistry of solutions there are endless factors to consider. Mixing between different liquids and solids vary depending on chemical structure, temperature, pressure, density and other properties (especially with water) that are unique to different compounds. In this report I will show you how to determine an estimate that will yield a very close result, specifically for water and sugar, but will also hold true for most other mixtures. METHODOLOGY Let's have a look at the calculations. 881*0.0296 = 26.054 g/fl. oz. If one cup is equal to 8 fluid ounces, then the mass of the sugar can be determined: 26.054*8 = 208.434 g. Converting these units to grams/fluid ounces: 1586.2*0.0296 = 46.909 g/fl. oz. We can now calculate the volume of one cup of sugar without all the "wasted space" between the granules (packing as if the sugar is a liquid): 208.434/46.909 = 4.443 fl. oz. Adding this value to the 8 fluid ounces occupied by the water alone gives us a total of 12.44 fluid ounces (8+4.44). EXTENDING THE METHOD If we had to generalize this method it would work as follows: 1. Find the packing density of the powder. 2. Packing density multiplied by volume gives you the mass of the powder. 3. The mass divided by the density of the powder gives you volume of perfect packing (as if it was a liquid). 4. Add this new found volume to the volume of the liquid to determine the total volume. It is extremely important to always make sure that you are working with the right units. Furthermore, I highly recommend that you do a test round first. For instance if you have to heat up your liquid to dissolve all of your powder then these volumes might change. Sugar added to water hot enough to dissolve the sugar would not increase the total volume the same amount as if it is added to cold water. CONCLUSION Mixing one cup water with one cup sugar will increase the total volume of the cup of water but it won't double the volume, the volume will be an estimated 12.44 fl. oz. (not 16 as one might expect). An estimate of the new volume can be made by using the packing density, volume and density of the powder.
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If a certain recipe takes 1 and 1/2 c of sugar and 4 c of water how much water should be added if the cook only has 1 c of sugar |
If you dissolve 1 cup of sugar in 4 cups of water what is the resulting volume of the mixture
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