Density of Lithium Metal: Calculate with D=m/V

In summary, density is a measure of mass per unit volume and is typically expressed in g/cm3 or kg/m3. To calculate density, divide the mass by the volume. The density of lithium metal is 0.534 g/cm3 or 534 kg/m3. The mass can be measured using a balance and the volume can be measured by submerging the metal in water. Calculating the density of lithium metal is important for determining its space and weight, which has applications in materials science, engineering, and chemistry.
  • #1
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Homework Statement


What is the density of lithium metal in g/cm^3 if a cylindrical wire with a diameter of 2.40mm and a length of 15.0cm has a mass of 0.3624g?

Homework Equations


D=m/V

The Attempt at a Solution


The problem I'm having is I don't understand what the problem is asking. How do you calculate the density of lithium metal with the diameter/length of a cylindrical wire and a the mass of the wire.
 
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  • #2
You're given the dimensions of the rod, you can calculate the volume.
 
  • #3


The density of a substance is defined as its mass per unit volume. In this case, the density of lithium metal can be calculated using the formula D=m/V, where D is the density, m is the mass, and V is the volume.

In the given problem, we are given the mass of the cylindrical wire (0.3624g) and its dimensions (diameter = 2.40mm and length = 15.0cm). To calculate the volume of the wire, we can use the formula for the volume of a cylinder, V=πr^2h, where r is the radius (half of the diameter) and h is the height (length).

So, for the given wire, the radius would be 1.20mm (2.40mm/2) and the height would be 15.0cm. Plugging these values into the formula, we get V=π(1.20mm)^2(15.0cm) = 67.020mm^3.

Next, we can plug the values for mass (0.3624g) and volume (67.020mm^3) into the formula for density, D=m/V. This gives us a density of 0.0054g/mm^3.

However, the given units for density are g/cm^3, so we need to convert mm^3 to cm^3. 1mm^3 is equal to 0.001cm^3, so 67.020mm^3 would be equal to 0.06702cm^3.

Therefore, the density of lithium metal in g/cm^3 would be 0.0054g/0.06702cm^3 = 0.0807g/cm^3.
 

1. What is density?

Density is a measure of the amount of mass per unit volume of a substance. It is usually expressed in units of grams per cubic centimeter (g/cm3) or kilograms per cubic meter (kg/m3).

2. How do you calculate density?

Density can be calculated by dividing the mass of a substance by its volume. In the case of lithium metal, the formula would be D=m/V, where D is density, m is mass, and V is volume.

3. What is the density of lithium metal?

The density of lithium metal is 0.534 grams per cubic centimeter (g/cm3) or 534 kilograms per cubic meter (kg/m3).

4. How do you measure the mass and volume of lithium metal?

The mass of lithium metal can be measured using a balance or scale, and the volume can be measured by submerging the metal in a graduated cylinder filled with water and recording the change in water volume.

5. Why is it important to calculate the density of lithium metal?

Knowing the density of lithium metal is important because it allows us to determine the amount of space it occupies and how much it weighs. This information is useful in various fields such as materials science, engineering, and chemistry.

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