Question

14 A metal block has a mass of 750 g. 60% of the mass is magnesium and the remainder is copper.

The density of magnesium is 1.7 g cm³.
The density of copper is 9.0 g cm³.
What is the density of the block?
A 2.5 g cm³.
B 4.6 g cm³.
C 5.4 g cm³.
D 10.7g cm³.

Answer 1

A

Step-by-step explanation:

To find the density of the metal block, we need to calculate the volume of the block and then divide the total mass by the volume.

Given:

Mass of the metal block = 750 g

Percentage of magnesium in the block = 60%

Percentage of copper in the block = 100% - 60% = 40%

Density of magnesium = 1.7 g/cm³

Density of copper = 9.0 g/cm³

Step 1: Calculate the mass of magnesium and copper in the block:

Mass of magnesium = 60% of 750 g = 0.60 * 750 g = 450 g

Mass of copper = 40% of 750 g = 0.40 * 750 g = 300 g

Step 2: Calculate the volume of magnesium and copper in the block:

Volume of magnesium = Mass of magnesium / Density of magnesium = 450 g / 1.7 g/cm³ ≈ 264.71 cm³

Volume of copper = Mass of copper / Density of copper = 300 g / 9.0 g/cm³ ≈ 33.33 cm³

Step 3: Calculate the total volume of the block:

Total volume = Volume of magnesium + Volume of copper = 264.71 cm³ + 33.33 cm³ ≈ 298.04 cm³

Step 4: Calculate the density of the block:

Density of the block = Total mass / Total volume = 750 g / 298.04 cm³ ≈ 2.52 g/cm³

So, the density of the metal block is approximately 2.52 g/cm³, which is closest to option A: 2.5 g/cm³.