To find the mass of gold that has the same volume as 12 grams of silver, we can follow these steps:
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Calculate the volume of silver.
Using the formula for density: \[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \Rightarrow \text{Volume} = \frac{\text{Mass}}{\text{Density}} \] For silver: \[ \text{Volume of silver} = \frac{12 \text{ g}}{10.49 \text{ g/cm}^3} \approx 1.143 \text{ cm}^3 \] -
Calculate the mass of gold that occupies the same volume.
Rearranging the density formula for mass: \[ \text{Mass} = \text{Density} \times \text{Volume} \] For gold with the volume calculated above: \[ \text{Mass of gold} = 19.32 \text{ g/cm}^3 \times 1.143 \text{ cm}^3 \approx 22.09 \text{ g} \]
Thus, the mass of gold that has the same volume as 12 grams of silver is approximately 22.09 grams.
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