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

22.10 g
22.10 g

1.84 g
1.84 g

2.202 g
2.202 g

21.08 g

Answer 1

To find the mass of gold that has the same volume as 12 grams of silver, we first need to calculate the volume of the silver using its density.

The formula for density is:

\[
\text{Density} = \frac{\text{Mass}}{\text{Volume}}
\]

From this, we can calculate volume as:

\[
\text{Volume} = \frac{\text{Mass}}{\text{Density}}
\]

Given the density of silver is 10.49 g/cm³, we can calculate the volume of 12 grams of silver:

\[
\text{Volume of silver} = \frac{12 \text{ g}}{10.49 \text{ g/cm}^3} \approx 1.144 \text{ cm}^3
\]

Now, we use the volume of silver to find the mass of gold that would occupy the same volume. Using the density of gold (19.32 g/cm³):

\[
\text{Mass of gold} = \text{Density} \times \text{Volume} = 19.32 \text{ g/cm}^3 \times 1.144 \text{ cm}^3
\]

Calculating this gives:

\[
\text{Mass of gold} \approx 22.10 \text{ g}
\]

Thus, the mass of gold that will have the same volume as 12 grams of silver is **22.10 g**.