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?(1 point)
Responses

2.202 g
2.202 g

21.08 g
21.08 g

1.84 g
1.84 g

22.10 g

Answer 1

To find the mass of gold that will have the same volume as 12 grams of silver, we first need to calculate the volume of the silver and then use the density of gold to find its mass.

1. **Calculate the volume of silver:**

Using the formula for volume:
\[
\text{Volume} = \frac{\text{Mass}}{\text{Density}}
\]

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

2. **Find the mass of gold that occupies this volume:**

Using the same formula for volume, rearranged to solve for mass:
\[
\text{Mass} = \text{Volume} \times \text{Density}
\]

For gold:
\[
\text{Mass of gold} = \text{Volume of gold} \times \text{Density of gold} = 1.143 \, \text{cm}^3 \times 19.32 \, \text{g/cm}^3 \approx 22.08 \, \text{g}
\]

Thus, the mass of gold that will have the same volume as 12 grams of silver is approximately **22.08 g**.

From the given responses, the closest option is **22.10 g**.