(a) To identify a liquid substance, a student determined its density. Using a graduated cylinder, she measured out a 45 -mL. sample of the substance. She then measured the mass of the sample, finding that it weighed 38.5 \(\mathrm{g}\) . She knew that the substance had to be either isopropylalcohol (density 0.785 \(\mathrm{g} / \mathrm{mL}\) )or toluene (density 0.866 \(\mathrm{g} / \mathrm{mL} ) .\) What are the calculated density and the probable identity of the substance? (b) An experiment requires 45.0 \(\mathrm{g}\) of ethylene glycol, a liquid whose density is 1.114 \(\mathrm{g} / \mathrm{mL}\) . Rather than weigh the sample on a balance, a chemist chooses to dispense the liquid using a graduated cylin-der. What volume of the liquid should he use? (c) Is a graduated cylinder such as that shown in Figure 1.21 likely to afford the accuracy of measurement needed? (d) A cubic piece of metal measures 5.00 \(\mathrm{cm}\) on each edge. If the metal is nickel, whose density is \(8.90 \mathrm{g} / \mathrm{cm}^{3},\) what is the mass of the cube?

Step by step solution

01

(a) Calculate the density of the liquid substance

To calculate the density of the substance, we will use the formula: \(Density = \frac{Mass}{Volume}\). In this case, mass = 38.5 g, and volume = 45 mL. Density = \(\frac{38.5\mathrm{g}}{45\mathrm{mL}}\) = 0.8555 g/mL.

02

(a) Determine the probable identity of the substance

We now need to identify if the substance is isopropyl alcohol (density 0.785 g/mL) or toluene (density 0.866 g/mL). Since the calculated density (0.8555 g/mL) is closer to the density of toluene, we can conclude that the substance is likely to be toluene.

03

(b) Calculate the volume of ethylene glycol required

In this part, we are given the mass of ethylene glycol (45 g) and its density (1.114 g/mL). We need to find the volume of the ethylene glycol. Using the formula for density, we can rearrange it to find the volume: \(Volume = \frac{Mass}{Density}\). Volume = \(\frac{45.0\mathrm{g}}{1.114\mathrm{g/mL}}\) = 40.4 mL.

04

(c) Comment on the accuracy of using a graduated cylinder

A graduated cylinder is likely to be less accurate than using a balance since it only measures volume rather than mass. Human error and inaccurate markings on the graduated cylinder can lead to small discrepancies in the measured volume. Therefore, it may not afford the desired accuracy of measurement in some cases.

05

(d) Calculate the mass of the nickel cube

In this part, we have a nickel cube with a side of 5 cm and a density of 8.90 g/cm³. To find the mass of the cube, we need to find its volume first: \(Volume = Side^3\). Volume = \((5.00\mathrm{cm})^3\) = 125 cm³. Now using the density of nickel (8.90 g/cm³), we can find the mass as: Mass = Density × Volume. Mass = \(8.90\mathrm{g/cm^3} \times 125\mathrm{cm^3}\) = 1112.50 g. So, the mass of the nickel cube is 1112.50 g.

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