To determine the approximate mass of a small spherical shot of copper, the following experiment is performed. When 125 pieces of the shot are counted out and added to \(8.4 \mathrm{mL}\) of water in a graduated cylinder, the total volume becomes \(8.9 \mathrm{mL}\). The density of copper is \(8.92 \mathrm{g} / \mathrm{cm}^{3} .\) Determine the approximate mass of a single piece of shot, assuming that all of the pieces are of the same dimensions.

Short Answer

Expert verified
The approximate mass of a single piece of shot is \(0.03568 \mathrm{g}\).

Step by step solution

01

Determine the Volume of the Shot Pieces

The volume of the shot pieces can be determined using volume displacement. When the shot pieces are added to the water, they displace a volume of water equal to their own volume. The initial volume of water was \(8.4 \mathrm{mL}\), and the final volume is \(8.9 \mathrm{mL}\). Therefore, the volume of the shot pieces is the difference, which is \((8.9-8.4) \mathrm{mL}=0.5 \mathrm{mL}\) or \(0.5 \mathrm{cm}^{3}\).
02

Calculate the Collective Mass of the Shot Pieces

The mass of the shot pieces can be calculated using the formula mass = volume × density, where the density of copper is given as \(8.92 \mathrm{g} / \mathrm{cm}^{3}\). So, the mass = \(0.5 \mathrm{cm}^3\) × \(8.92 \mathrm{g} / \mathrm{cm}^3\)= 4.46 g.
03

Calculate the Mass of a Single Shot Piece

To calculate the mass of a single shot piece, divide the total mass by the number of pieces. Hence, the mass of a single shot piece is \(4.46 \mathrm{g} / 125 = 0.03568 \mathrm{g}\).

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