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A glass vessel weighs $\pu{20.2367 g}$ when empty and $\pu{20.3102 g}$ when filled to the etched mark with water at $\pu{4 °C}$. The same vessel was then dried and filled to the same mark with a solution at $\pu{4 °C}$, the vessel was now found to weigh $\pu{20.3300 g}$. What is the density of the solution? (Assume the density of water is $\pu{1.00 g/ml}$)

Here’s what I did:

The mass of the water is just $\pu{0.0735 g}$ when you subtract the weight of (water + vessel) and (empty vessel). Then I found how many $\pu{ml}$ of water there was in the vessel by realizing that the density ($m/V$) must be equal to $1$, so $\pu{0.0735 g}$ of water must be $\pu{0.0735 ml}$ of water too. So with that, I figured out how many grams of the unknown solution were in the vessel ($\pu{0.0993 g}$), and knowing that it was filled to the same “etched mark,” we can say that the density of the unknown solution is $\pu{0.0933 g}/\pu{0.0735 ml} = \pu{1.27 g/ml}$. I went through all of that because I am not sure if my thoughts are on track with logic and I am pretty confused.

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  • $\begingroup$ Please read this $\endgroup$ – Freddy Sep 14 '14 at 18:13
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    $\begingroup$ Your answer is correct. Density=mass/volume In the water experiment you know density and mass, therefore you can calculate the volume of the vessel. In the second experiment you know the mass, along with the volume from the first experiment, so you can calculate the density. $\endgroup$ – ron Sep 14 '14 at 18:26
  • $\begingroup$ Thanks so much for taking the time to look over that. It means a lot, thank you! $\endgroup$ – user3138766 Sep 14 '14 at 18:27
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    $\begingroup$ This is a good example of how a HW question should be written. $\endgroup$ – LordStryker Sep 15 '14 at 19:41
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What you did in your explanation is correct. First find the difference in the weight: $$20.3102-20.2367=0.0735 \ \mathrm{g}$$

We know that from your density of water: $\mathrm{\frac{1\ g}{1\ mL}\ \text{that }\ 0.0735 \ g = 0.0735\ mL}$

Then the difference between the unknown and the vessel is calculated as: $$20.300-20.2367 = 0.0933\ \mathrm{g}$$

and then density is expressed as mass over volume, so: $$\mathrm{\frac{0.0933\ g}{0.0735\ mL}=1.2693_8\ g\ mL^{-1}}$$

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