The karat is a dimensionless unit that is used to indicate the proportion of gold in a gold-containing alloy. An alloy that is one karat gold contains a weight of pure gold that is one part in twenty-four. What is the volume of gold in a 20.0-karat gold necklace whose weight is 1.50 N?
To find the volume of gold in a 20.0-karat gold necklace, you need to know the weight of the necklace and the proportion of gold in it.
First, you need to convert the weight of the necklace from Newtons (N) to a more common unit like grams (g) or kilograms (kg). Let's assume you are converting it to grams.
1. Convert weight from Newtons to grams:
- Recall that 1 Newton is equal to 1000 grams.
- Multiply the weight in Newtons by 1000 to convert it to grams.
- Let's say the weight of the necklace is 1.50 N.
- 1.50 N * 1000 g/N = 1500 g
Next, you need to determine the weight of pure gold in the necklace based on its karat value.
2. Determine the weight of pure gold:
- According to the given information, a 20.0-karat gold alloy contains a weight of pure gold that is one part in twenty-four.
- In other words, for every 24 parts of the alloy, one part is pure gold.
- Therefore, the weight of pure gold in the necklace can be calculated as:
1500 g * (1/24) = 62.5 g
Finally, you can calculate the volume of pure gold using its density.
3. Calculate the volume of pure gold:
- Gold has a known density of 19.3 g/cm³.
- The formula for volume is: Volume = Mass / Density.
- Substituting the values, we get:
Volume = 62.5 g / 19.3 g/cm³ ≈ 3.24 cm³
Therefore, the volume of gold in the 20.0-karat gold necklace weighing 1.50 N is approximately 3.24 cm³.