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
1.84 g
1.84 g
21.08 g
21.08 g
2.202 g
2.202 g
22.10 g
What mass of gold will have the same volume as 12 grams of silver?
(1 point)
Responses
1.84 g
1.84 g
21.08 g
21.08 g
2.202 g
2.202 g
22.10 g
Answers
GPT-4o mini
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.
1. **Calculate the volume of silver** using its density:
\[
\text{Volume of silver} = \frac{\text{mass}}{\text{density}} = \frac{12 \, \text{g}}{10.49 \, \text{g/cm}^3} \approx 1.144 \, \text{cm}^3
\]
2. **Now calculate the mass of gold** that occupies the same volume:
\[
\text{Mass of gold} = \text{Volume} \times \text{Density of gold} = 1.144 \, \text{cm}^3 \times 19.32 \, \text{g/cm}^3 \approx 22.10 \, \text{g}
\]
Therefore, the mass of gold that will have the same volume as 12 grams of silver is **22.10 g**.
1. **Calculate the volume of silver** using its density:
\[
\text{Volume of silver} = \frac{\text{mass}}{\text{density}} = \frac{12 \, \text{g}}{10.49 \, \text{g/cm}^3} \approx 1.144 \, \text{cm}^3
\]
2. **Now calculate the mass of gold** that occupies the same volume:
\[
\text{Mass of gold} = \text{Volume} \times \text{Density of gold} = 1.144 \, \text{cm}^3 \times 19.32 \, \text{g/cm}^3 \approx 22.10 \, \text{g}
\]
Therefore, the mass of gold that will have the same volume as 12 grams of silver is **22.10 g**.