Question

Ethyl alcohol has a density of \(0.79 \mathrm{~g} / \mathrm{mL}\). What is the volume, in quarts, of \(1.50 \mathrm{~kg}\) of alcohol?

Short answer

2.005 quarts.

Step-by-step solution

Convert mass to grams

Given mass is 1.50 kg. Convert the mass to grams using the conversion factor: 1 kg = 1000 g.So, \[1.50 \text{ kg} \times 1000 \frac{ \text{ g} }{ \text{kg} } = 1500 \text{ g}\]

Use density to find volume in mL

Density (\rho) of ethyl alcohol is 0.79 g/mL, and the mass (m) is 1500 g. Use the formula for density: \[\rho = \frac{m}{V}\]Rearrange to solve for volume (V): \[V = \frac{m}{\rho} = \frac{1500 \text{ g}}{0.79 \text{ g/mL}} = 1898.73 \text{ mL}\]

Convert mL to quarts

To convert from milliliters to quarts, use the conversion factor:1 L = 1000 mL and 1 L ≈ 1.05669 quarts.First, convert mL to liters: \[1898.73 \text{ mL} \times \frac{1 \text{ L}}{1000 \text{ mL}} = 1.89873 \text{ L}\]Then, convert liters to quarts: \[1.89873 \text{ L} \times 1.05669 \frac{ \text{ quarts} }{ \text{ L} } = 2.005 \text{ quarts}\]

Key concepts

mass to volume conversion

Converting mass to volume is a common task in chemistry and physics. The core idea involves using the density of a substance to determine how much space a given mass will occupy.

Here’s a simple step-by-step guide to help you understand this better:

• Start with the given mass. In our exercise, we have 1.50 kg of ethyl alcohol.
• First, convert this mass into grams, since density is usually given in g/mL. Use the conversion factor 1 kg = 1000 g, so 1.50 kg becomes 1500 g.
• Once you have the mass in grams, use the density formula to find the volume. The formula for density is \(\rho = \frac{m}{V}\), where \(m\) is mass and \(V\) is volume. Rearrange this formula to solve for volume (V): \(\frac{m}{\rho}\).
  
  

Using the given density of ethyl alcohol (0.79 g/mL), we calculate the volume by dividing the mass by the density: \(\frac{1500 g}{0.79 g/mL} \approx 1898.73 mL\).

density formula

The density formula is an essential concept in science, helping to relate a substance's mass and volume. It's denoted by the symbol \(\rho\) (Greek letter rho). The formula is:
\(\rho = \frac{m}{V}\), where:

• \(m\) represents mass, typically measured in grams (g) or kilograms (kg).
• \(V\) represents volume, often measured in milliliters (mL) or liters (L).
• \(\rho\) (density) is the ratio of mass to volume, usually in g/mL or kg/L.

To use this formula:

• First, determine the mass (\(m\)) and density (\(\rho\)) of the substance.
• Then, rearrange the formula to solve for volume (\(V\)): \(\frac{m}{\rho}\).

In our exercise, we used the density (0.79 g/mL) and mass (1500 g) of ethyl alcohol to find the volume:
\(\frac{1500 g}{0.79 g/mL} \approx 1898.73 mL \). This formula helps in understanding how much space a certain amount of matter will occupy.

unit conversion

Unit conversion is an essential skill for solving scientific problems. It allows us to switch between different units of measurement, making it easier to use given data in calculations.

In our exercise, we converted between multiple units:

• Mass Conversion: We first converted the mass from kilograms (kg) to grams (g) using the conversion factor 1 kg = 1000 g.
• Volume Conversion: After finding the volume in milliliters (mL), we converted it to liters (L) using the conversion 1 L = 1000 mL. Then, we further converted liters to quarts using the conversion factor 1 L ≈ 1.05669 quarts.

The steps for volume conversion were:

• Convert mL to L: \(\frac{1898.73 mL}{1000} = 1.89873 L\)
• Convert L to quarts: \(\frac{1.89873 L \times 1.05669}{1} = 2.005 quarts\)

Understanding these conversions ensures you can accurately interpret and use scientific data presented in various units.