Question

3) You have a sample of titanium, copper, and lead wire (all the same gauge, or diameter). Your lab group measured a length of wire that is exactly 10.00g for each type of metal wire. a) Which of these 3 metal wires would be the longest? Explain how you determined your answer. b) Which of these 3 metal wires would be the shortest? Explain how you determined your answer. Refer to the table of densities ABOVE to answer these questions: d) If every 1.0 cm length of the titanium wire has a mass of 0.15 g, how long would the 10.00g wire be? (Hint: Write a conversion ratio for the two quantities you are working with)​

Answer 1

To determine which of the three metal wires is the longest, we can compare their densities. Density is defined as mass divided by volume (density = mass/volume). Since all the wires have the same mass (10.00 g), the one with the lowest density will have the largest volume, and therefore, it will be the longest.

a) Titanium has the lowest density among the three metals, so the titanium wire would be the longest. This is because with the same mass, a lower density metal occupies a larger volume.

b) Lead has the highest density among the three metals, so the lead wire would be the shortest. Higher density means the same mass occupies a smaller volume.

c) To find the length of the 10.00 g titanium wire, we can use the density and rearrange the density formula: density = mass/volume, so volume = mass/density.

Given that the density of titanium is 4.51 g/cm³, we can calculate the volume:

Volume = 10.00 g / 4.51 g/cm³ ≈ 2.215 cm³

Now, we can find the length of the wire by dividing the volume by the cross-sectional area. Since the wire is cylindrical, we need to know its diameter (gauge) to calculate the cross-sectional area. Without that information, we can't find the exact length. If you have the diameter, you can use the formula for the volume of a cylinder (V = πr²h), where "r" is the radius and "h" is the length of the wire, to find the length of the titanium wire.