Question

What is the density of a 12.475g piece of metal that causes the level of water in a graduated cylinder to rise from 5.0 to 6.1 mL when the metal is submerged in the water?

Consider significant figures when doing the calculation.

Answer 1

The density of the metal is calculated using the mass and volume displacement in a graduated cylinder. The volume is 1.1 mL as determined by the change in water level, and with a mass of 12.475 grams, the density is 11.3 g/mL considering significant figures.

Step-by-step explanation:

The student is asking how to calculate the density of a metal based on the displacement of water in a graduated cylinder. To find the density, we use the formula:

Density = mass/volume

Firstly, we determine the volume of the metal by the water displacement method, which is the final water level (6.1 mL) minus the initial water level (5.0 mL). Therefore, the volume of the metal is 6.1 mL - 5.0 mL = 1.1 mL. As water has a density of 1 g/mL, the displacement in milliliters can be directly used to represent the volume of the metal in cubic centimeters. The given mass of the metal is 12.475 grams.

Applying the formula:

Density = 12.475 grams / 1.1 mL = 11.34 grams per milliliter

Considering significant figures, this would be reported as 11.3 g/mL, since the volume measurement is only precise to the tenths place.

Answer 2

11.3 g/mL.

Step-by-step explanation:

• Density is a characteristic property of a substance.

• The density of a substance is the relationship between the mass of the substance and the volume it takes up.

d = m/V,

where, d is the density of the metal,

m is the mass of the metal (m = 12.475 g),

V is the volume that the metal takes up (V = 6.1 mL - 5.0 mL = 1.1 mL).

∴ d = m/V = (12.475 g)/(1.1 mL) = 11.34 g/mL ≅ 11.3 g/mL.

The significant figures has its rules in the calculations; the result has a significant figures to the lowest no. of significant figures (1.1 has two significant figures, while 12.475 has 5 significant figures), so the result should have only 2 significant figures.