Question

density calculations
density is the ration of mass to volume within a substance. it is the only way to convert between mass and volume.
calculate the solution to the following density problems using the equations below:

\\( \text{density} = \frac{\text{mass}}{\text{volume}} \\) \\( d = \frac{m}{v}

1. a block of aluminum has a mass of 54.0 grams and a volume of 20.0 milliliters. what is the density of aluminum?

1. the density of gold is 19.3 grams per cubic centimeter (cm³). what volume in cm³ would 95.9 grams of gold occupy?

1. if the density of silver is 10.5 g/ml, what would be the mass of 750 milliliters of silver?

1. a 125 milliliter container of rubbing alcohol has a mass of 98.25 grams. what is the density of rubbing alcohol?

1. a 375 gram block of ice is frozen. what volume will the ice occupy if the density of ice is 0.931 g/cm³?

1. red oak has a density of 0.740 grams per milliliter. what would be the mass of a 1000 ml block of oak?

Explanation:

Problem 1

Step1: Identify formula

We use the density formula \( D=\frac{m}{V} \), where \( m = 54.0\space g \) and \( V=20.0\space mL \).

Step2: Substitute values

Substitute \( m = 54.0 \) and \( V = 20.0 \) into the formula: \( D=\frac{54.0}{20.0} \)

Step3: Calculate

\( \frac{54.0}{20.0}=2.70\space g/mL \)

Step1: Rearrange formula

From \( D=\frac{m}{V} \), we get \( V = \frac{m}{D} \), where \( m = 95.9\space g \) and \( D = 19.3\space g/cm^3 \).

Step2: Substitute values

Substitute \( m = 95.9 \) and \( D=19.3 \) into the formula: \( V=\frac{95.9}{19.3} \)

Step3: Calculate

\( \frac{95.9}{19.3} \approx 4.97\space cm^3 \)

Step1: Rearrange formula

From \( D=\frac{m}{V} \), we get \( m=D\times V \), where \( D = 10.5\space g/mL \) and \( V = 750\space mL \).

Step2: Substitute values

Substitute \( D = 10.5 \) and \( V = 750 \) into the formula: \( m=10.5\times750 \)

Step3: Calculate

\( 10.5\times750 = 7875\space g \)

Answer:

\( 2.70\space g/mL \)

Problem 2