Question

The density of silver is 10.49 g/cm3 , and the density of gold is 19.32 g/cm3 . What mass of gold will have the same volume as 12 grams of silver?

Answer 1

To find the mass of gold that has the same volume as 12 grams of silver, we can follow these steps:

1. **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:
\[
\text{Volume of silver} = \frac{12 \text{ g}}{10.49 \text{ g/cm}^3} \approx 1.143 \text{ cm}^3
\]

2. **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**.