Question

The density of silver is 10.49 g/cm^3, and the density of gold is 19.32 g/cm^3. What mass of gold will have the same volume as 12 grams of silver?

a. 22.10 g
b. 21.08 g
c. 1.84 g
d. 2.202 g

Answer 1

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

1. First, calculate the volume of 12 grams of silver using its density:

\[
\text{Density of silver} = 10.49 \, \text{g/cm}^3
\]

\[
\text{Volume of silver} = \frac{\text{Mass of silver}}{\text{Density of silver}} = \frac{12 \, \text{g}}{10.49 \, \text{g/cm}^3}
\]

Calculating the volume:

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

2. Next, use the volume of silver to find the corresponding mass of gold using its density:

\[
\text{Density of gold} = 19.32 \, \text{g/cm}^3
\]

Using the volume of silver, we can find the mass of gold:

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

Calculating the mass of gold:

\[
\text{Mass of gold} \approx 19.32 \times 1.144 \approx 22.10 \, \text{g}
\]

Therefore, the mass of gold that will have the same volume as 12 grams of silver is:

**a. 22.10 g**