Question

a vessel contains 30 ml of water. a sample of 5.0 g of copper metal is dropped into this vessel, raising the level of water in it to 40 ml. calculate the density of the copper sample.

Explanation:

Step1: Find the volume of the copper sample

The initial volume of water is 30 mL, and after adding the copper, the volume is 40 mL. The volume of the copper is the difference in water levels. So, \( V = 40\ mL - 30\ mL = 10\ mL \). Since \( 1\ mL = 1\ cm^3 \), the volume \( V = 10\ cm^3 \).

Step2: Calculate the density of the copper sample

Density is given by the formula \(
ho=\frac{m}{V} \), where \( m \) is the mass and \( V \) is the volume. The mass of the copper \( m = 5.0\ g \) and the volume \( V = 10\ cm^3 \). Substituting these values into the formula, we get \(
ho=\frac{5.0\ g}{10\ cm^3}=0.5\ g/cm^3 \)? Wait, no, wait. Wait, copper's density is actually around 8.96 g/cm³, but let's check the calculation again. Wait, initial volume 30 mL, final 40 mL, so volume of copper is 40 - 30 = 10 mL = 10 cm³. Mass is 5.0 g? Wait, that can't be right, maybe a typo? Wait, no, the problem says 5.0 g? Wait, no, maybe I misread. Wait, the problem says "a sample of 5.0 g of copper metal"? Wait, that would make density 0.5 g/cm³, which is wrong. Wait, maybe it's 50.0 g? Wait, no, the problem as given: "A vessel contains 30 mL of water. A sample of 5.0 g of copper metal is dropped into this vessel, raising the level of water in it to 40 mL. Calculate the density of the copper sample." So according to the problem, mass is 5.0 g, volume is 10 mL. So density \(
ho=\frac{5.0\ g}{10\ mL}=0.5\ g/mL \) (or \( 0.5\ g/cm^3 \)). But that's not correct for copper, but maybe the problem has a typo. But following the problem's numbers:

So step 1: Volume of copper = final volume - initial volume = 40 mL - 30 mL = 10 mL.

Step 2: Density \(
ho=\frac{m}{V}=\frac{5.0\ g}{10\ mL}=0.5\ g/mL \) (or \( 0.5\ g/cm^3 \)).

Wait, but maybe the mass is 50 g? Let me check again. The problem says 5.0 g. So maybe it's a hypothetical problem. So proceeding with the given numbers.

Answer:

The density of the copper sample is \( 0.5\ g/cm^3 \) (or \( 0.5\ g/mL \)).