Use the 5-step method and be sure to include units where appropriate. Round your answers to the correct number of significant digits.
Mass m
Density = -------------- or D = -------
Volume v
Adjust the density formula and solve the problems below:
m
D = ------- Original Formula
v
Adjust the formula for the unknown v =
1. Pure gold has a density of 119.32 g/cm3. How large would a piece of gold be if it had a mass of 3118.97 g?
2. How many cm3 would a 515.932 g sample of copper occupy if it has a density of 18.92 g/cm3?
3. The density of lead is 111.342 g/cm3. What would be the volume of a 200.0 g sample of this metal?
To solve these problems using the density formula, follow the 5-step method:
Step 1: Identify the given values and what you are trying to find.
Step 2: Write down the formula for density.
Step 3: Rearrange the formula to solve for the unknown variable.
Step 4: Substitute the given values into the formula.
Step 5: Calculate the value of the unknown variable, making sure to round to the appropriate number of significant digits and include units.
Let's solve the problems using this method:
Problem 1:
Given: Density (D) = 119.32 g/cm^3, Mass (m) = 3118.97 g
Unknown: Volume (v)
Step 1: Given values are the density (D) and mass (m). We need to find the volume (v).
Step 2: The formula for density is D = m/v.
Step 3: Rearranging the formula, we get v = m/D.
Step 4: Substitute the given values: v = 3118.97 g / 119.32 g/cm^3.
Step 5: Calculate the value: v = 26.12 cm^3 (rounded to 3 significant digits).
Therefore, the piece of gold would have a volume of 26.12 cm^3 if it had a mass of 3118.97 g.
Problem 2:
Given: Density (D) = 18.92 g/cm^3, Mass (m) = 515.932 g
Unknown: Volume (v)
Step 1: Given values are the density (D) and mass (m). We need to find the volume (v).
Step 2: The formula for density is D = m/v.
Step 3: Rearranging the formula, we get v = m/D.
Step 4: Substitute the given values: v = 515.932 g / 18.92 g/cm^3.
Step 5: Calculate the value: v = 27.25 cm^3 (rounded to 3 significant digits).
Therefore, the 515.932 g sample of copper would occupy a volume of 27.25 cm^3.
Problem 3:
Given: Density (D) = 111.342 g/cm^3, Mass (m) = 200.0 g
Unknown: Volume (v)
Step 1: Given values are the density (D) and mass (m). We need to find the volume (v).
Step 2: The formula for density is D = m/v.
Step 3: Rearranging the formula, we get v = m/D.
Step 4: Substitute the given values: v = 200.0 g / 111.342 g/cm^3.
Step 5: Calculate the value: v = 1.796 cm^3 (rounded to 3 significant digits).
Therefore, the 200.0 g sample of lead would have a volume of 1.796 cm^3.