In an experiment, \(125 \mathrm{cm}^{3}\) of zinc and \(125 \mathrm{cm}^{3}\) of iodine are mixed together and the iodine is completely converted to \(164 \mathrm{cm}^{3}\) of zinc iodide. What volume of zinc remains unreacted? The densities of zinc, iodine, and zinc iodide are \(7.13 \mathrm{g} / \mathrm{cm}^{3}, 4.93 \mathrm{g} / \mathrm{cm}^{3}\) and \(4.74 \mathrm{g} / \mathrm{cm}^{3}\), respectively.

Short Answer

Expert verified
The volume of unreacted zinc is approximately \(102.42 \mathrm{cm^{3}}\).

Step by step solution

01

Calculate the Mass of the Initial Substances

Use the volumes and densities of the initial substances (zinc and iodine) to calculate their masses. The mass is simply the volume times the density. Therefore, the mass of zinc and iodine can be calculated as: Mass_Zn = \(7.13 \mathrm{g/cm^3} \times 125 \mathrm{cm^3} = 891.25g\) Mass_I = \(4.93 \mathrm{g/cm^3} \times 125 \mathrm{cm^3} = 616.25g\)
02

Calculate the Total Mass Before the Reaction

Add the masses of zinc and iodine calculated in Step 1 to get the total mass before the reaction: Total mass before = \(891.25g + 616.25g = 1507.5g\)
03

Calculate the Mass of Zinc Iodide After the Reaction

Using the volume and density of zinc iodide, calculate its mass: Mass_ZnI2 = \(4.74 \mathrm{g/cm^3} \times 164 \mathrm{cm^3} = 777.16g\)
04

Calculate the Mass of Unreacted Zinc

Subtract the mass of zinc iodide from the total mass before the reaction to find the mass of the unreacted zinc: Mass_Zn(unreacted) = \(1507.5g - 777.16g = 730.34g\)
05

Convert the Mass of Unreacted Zinc to Volume

Use the density of zinc to convert the mass of the unreacted zinc to volume. Volume = mass / density. Thus, Volume_Zn(unreacted) = \(730.34g / 7.13 \mathrm{g/cm^3} = 102.42 \mathrm{cm^3}\)

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