To find the mass of gold that has the same volume as 12 grams of silver, we first need to determine the volume of the silver and then use that volume to calculate the mass of gold.
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Calculate the volume of silver:
The formula for volume is:
\[ \text{Volume} = \frac{\text{mass}}{\text{density}} \]
For silver, with a mass of 12 grams and a density of 10.49 g/cm³:
\[ \text{Volume of silver} = \frac{12 , \text{g}}{10.49 , \text{g/cm}^3} \approx 1.144 , \text{cm}^3 \]
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Calculate the mass of gold using the same volume:
Now we can find the mass of gold that occupies this volume. Using the density of gold (19.32 g/cm³):
\[ \text{Mass of gold} = \text{Volume} \times \text{Density} \]
\[ \text{Mass of gold} = 1.144 , \text{cm}^3 \times 19.32 , \text{g/cm}^3 \approx 22.08 , \text{g} \]
Thus, the mass of gold that will have the same volume as 12 grams of silver is approximately 22.08 g. Based on the provided options, the closest answer is 22.10 g.