To determine the volume of an irregularly shaped glass vessel, the vessel is weighed empty \((121.3 \mathrm{g})\) and when filled with carbon tetrachloride (283.2 g). What is the volume capacity of the vessel, in milliliters, given that the density of carbon tetrachloride is \(1.59 \mathrm{g} / \mathrm{mL} ?\)

Short Answer

Expert verified
The volume capacity of the vessel is 101.89 mL.

Step by step solution

01

Determine the mass of carbon tetrachloride

This is done by subtracting the weight of the empty vessel from the weight of the vessel when filled with carbon tetrachloride. So, \(mass_{carbon\ tetrachloride} = weight_{filled\ vessel} - weight_{empty\ vessel}\) = \(283.2 g - 121.3 g\) = \(161.9 g\)
02

Apply density formula to find the volume

We know that density = mass/volume. By rearranging, we get volume = mass/density. Hence, \(volume_{carbon\ tetrachloride} = mass_{carbon\ tetrachloride} / density_{carbon\ tetrachloride}\) = \(161.9g / 1.59 g/mL\) = \(101.885 mL\)
03

Round to appropriate significant figures

Considering the provided values in the problem, the measurement with the least number of decimal places is of two places, hence we need to round our answer to two decimal places. Therefore, \( volume_{final} = 101.89 mL\)

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