a. What is the specific gravity of the following solution?

Question

Accepted Answer

Welcome back, everyone. We need to determine the reading reported when the specific gravity of the solution below was determined using a hydrometer. And we are given the following image of a solution where we've got our hydrometer placed in the middle of a body of water, which we are measuring the specific gravity of. Now, let's recall what specific gravity is defined as specific gravity. We should recall is going to correlate to the density of a substance or a solution which is divided by the density of water. And this is all at the same temperature recall that specific gravity is going to be unless and we can determine specific gravity of a liquid using a hydrometer. And so that is what is depicted in our image is a rough sketch of a hydrometer where we should recall a hydrometer is going to be an instrument that has a weighted bulb at the end of a calibrated glass tube. So we can observe the calibrated glass tube in our given image and when placed inside of a fluid, it's going to sink to a depth indicating the specific gravity of the fluid we are measuring. So the deeper the bulb sinks will correlate to a lower fluid specific gravity. Whereas the higher the hydrometer floats, the higher the fluid specific gravity would be. So we're going to first first observe that we've got two measurements depicted on the hydrometer which we will interpret as the larger calibrations. So the larger calibrations given on the hydrometer are mark marked as 0. and then 0.980. So these define the larger divisions on the scale of our hydrometer that is depicted in our given image. And we also have these smaller ticks which are defining the smaller incremental units between our larger calibration units. And so the level of intersection for our fluid that we are measuring is going to be between these two larger calibrations. But we need to read this to accurate with accuracy. And so if we go ahead and now include the smaller incremental units on the hydrometer, we're going to place at the first tick mark above 0.990, a measurement of 0.988. And above the mark of 0.988, we can fill in 0.9 986 above that we can fill in 0.984. And then above that, we can fill in 0.982. And so separating each of these increments, we've got steps of 0.2. Now, as we stated earlier, in order to properly measure the specific gravity of our fluid. Using the hydrometer, we're going to need to make an accurate reading by looking at the plain of intersection of the horizontal liquid surface and the stem of our hydrometer. And so the horizon horizontal liquid surface of our fluid, we would depict at an eyes view at this location where we have the first hori horizontal marking of the surface of our fluid. And we can read this at a level based on the smaller increments that we filled in of 0.986. So that marks the horizontal plane of intersection of the horizontal surface of our liquid and the stem of our hydrometer 0.986. So because we stated that our increments between the readings on the hydrometer are about 0.2. So we got 00, sorry 0.2 increments on the hydrometer. We can also note that we have the level of horizontal surface of the liquid or of the fluid and intersection with the hydrometer at 0.986. And so based on the ticks expressed on the hydrometer, that is a total of 123 ticks total to get from the larger calibration of 1230.990 to the smaller increment of 0.986. So, so in parentheses, we can write three minor divisions below 0.990, our larger calibration on the hydrometer. And so if we know that we've got 0.2 increments separating the readings on this hydrometer. We can take the three minor divisions multiplied by 0.2. And that will equal the level of our horizontal surface of our fluid as 0.6 as an increment. So with that outlined and sorry, just to make a correction. So we've got two increments above our larger calibration 0.990 to get to the horizontal level of the surface of our fluid. And so it should actually be two times 0.2, which is our increment separating each reading. And that would give us then a value of 0.4 as the level of the fluid as an increment using the hydrometer readings that we filled in. And so ultimately, if we then take our larger calibration of 0. and subtract that from zero and subtract 0. from that, that confirms that we are properly getting a precise measure for the specific gravity of our fluid as 0.986. And that would be the final reading. So in this final reading, we can confirm that 0.98, specifically the nine and the eight would be our precise and known numbers. And the six included at the end is going to be an estimated digit for a enhanced precision of our reading. And if we recall the density of water recall that the density of water is equal to about one point oh gram per milliliter. And although specific gravity doesn't have units 1.0.986 is less than one point oh grams per milliliter. And so this reading of the fluid in our image is less than the density of water. So it's less dense than water. So ultimately, our final answer is going to be the reading that we determined as the specific gravity of the fluid being 0.986. I hope that this made sense and let us know if you have any questions.

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a. What is the specific gravity of the following solution?

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