Question

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 14.0-karat gold necklace whose weight is 1.25 N?

Answer 1

To find the volume of gold in a 14-karat gold necklace, calculate the mass of the necklace from its weight, determine the mass of pure gold based on the karat, and divide by the density of gold, which is 19.3 g/cm³.

Step-by-step explanation:

The volume of gold in a 14.0-karat gold necklace weighing 1.25 N can be determined by first calculating the mass of the necklace using the acceleration due to gravity (9.8 m/s2), and then using the proportion of gold in the 14-karat alloy to find the mass of pure gold. The density of gold is known to be 19.3 g/cm3, which allows us to find the volume by dividing the mass of pure gold by the density.

Steps to Calculate the Volume of Gold:

Calculate the mass of the necklace:
M = F/g, where F is the force in newtons and g is 9.8 m/s2.

Calculate the mass of pure gold in the necklace: mass of gold = total mass × (14/24) since 14-karat means 14 parts gold out of 24.

Calculate the volume of pure gold in the necklace: V = mass of gold / density of gold.

Following the above steps will yield the volume of gold in the necklace, answering the original question.

Answer 2

Volume,
`V=3.78* 10^(-6)\ m^3`

Step-by-step explanation:

It is given that, an alloy that is one karat gold contains a weight of pure gold that is one part in twenty-four.

14 karat of gold contains a weight of pure gold is,
`(14)/(24)=0.58`

The necklace contains 58% of gold, the weight of gold is :

`W=0.58* 1.25=0.725\ N`

The mass of gold is,
`m=(0.725)/(9.8)=0.073\ kg`

Let V is the volume of fold in 14 karat. Using the formula of density to find it as :

`d=(m)/(V)`

`V=(m)/(d)`

d is the density of gold,
`d=19300\ kg/m^3`

`V=(0.073\ kg)/(19300\ kg/m^3)`

`V=3.78* 10^(-6)\ m^3`

So, the volume of fold necklace is
`3.78* 10^(-6)\ m^3`. Hence, this is the required solution.