A nugget of gold with a mass of 521 g is added to 50.0 mL of water. The water level rises to a volume of 77.0 mL. What is the density of the gold?
A) 10.4 g/mL
B) 6.77 g/mL
C) 1.00 g/mL
D) 0.0518 g/mL
E) 19.3 g/mL
The correct answer and explanation is :
To determine the density of the gold nugget, we use the density formula:
[
\text{Density} = \frac{\text{Mass}}{\text{Volume}}
]
Step 1: Determine the mass of the gold
From the question:
- Mass of the gold = 521 g
Step 2: Determine the volume of the gold
Since the nugget is placed into water and causes the water level to rise, we can find the volume of the gold using water displacement:
- Initial volume of water = 50.0 mL
- Final volume after adding gold = 77.0 mL
[
\text{Volume of gold} = 77.0\, \text{mL} – 50.0\, \text{mL} = 27.0\, \text{mL}
]
Step 3: Calculate the density
[
\text{Density} = \frac{521\, \text{g}}{27.0\, \text{mL}} \approx 19.3\, \text{g/mL}
]
✅ Correct Answer: E) 19.3 g/mL
🔍 Explanation (300+ words):
Density is a physical property of matter that relates an object’s mass to its volume. It tells us how compact or concentrated the material in an object is. The formula for density is:
[
\text{Density} = \frac{\text{Mass}}{\text{Volume}}
]
In this problem, the mass of the gold is given as 521 grams. However, we are not directly given the volume of the gold nugget. Instead, the displacement method is used. This method is based on Archimedes’ principle, which states that when an object is submerged in a fluid, it displaces a volume of fluid equal to its own volume.
By placing the gold nugget in water, the volume rises from 50.0 mL to 77.0 mL, meaning the gold has displaced 27.0 mL of water. This displacement tells us that the volume of the gold is 27.0 mL.
Now using the formula:
[
\text{Density} = \frac{521\, \text{g}}{27.0\, \text{mL}} \approx 19.3\, \text{g/mL}
]
This result is very close to the known density of pure gold, which is 19.3 g/mL, confirming the accuracy of the calculation and supporting that the object is indeed gold.
The other answer choices:
- A (10.4), B (6.77), and C (1.00) are typical of other materials like metals, water, or organic substances.
- D (0.0518) is far too low and likely results from misplacing the decimal.
Thus, Option E is the correct and most reasonable answer based on both calculation and real-world reference.