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Chapter 1: Problem 24

The density of ethanol, a colorless liquid that is commonly known as grain alcohol, is \(0.798 \mathrm{~g} / \mathrm{mL}\). Calculate the mass of \(205 \mathrm{~mL}\) of the liquid.

Short Answer

Expert verified
The mass of 205 mL of ethanol is 163.59 g.

Step by step solution

01

Understanding the Formula

To find the mass of a substance when its density and volume are known, we use the formula: \[ \text{Mass} = \text{Density} \times \text{Volume} \] Density, in this case, is given as \(0.798\, \mathrm{g/mL}\), and volume is given as \(205\, \mathrm{mL}\).
02

Plugging Values into the Formula

Now that we know both the density and the volume, we can substitute these values into the formula: \[ \text{Mass} = 0.798\, \mathrm{g/mL} \times 205\, \mathrm{mL} \]
03

Performing the Calculation

Multiply the density by the volume: \[ 0.798 \times 205 = 163.59 \] Thus, the mass of the ethanol is \(163.59\, \mathrm{g}\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Mass Calculation
Mass calculation is a fundamental concept in chemistry that allows you to determine how much of a substance you have. When you know the density of the substance and its volume, you can easily calculate the mass. The formula used for this purpose is \( \text{Mass} = \text{Density} \times \text{Volume} \). This means the mass is just the product of density and volume.

Let's say you have 205 mL of ethanol, and you are given that the density of ethanol is 0.798 g/mL. You can directly use the formula to find the mass. Plug the values you have into the equation:
  • Density = 0.798 g/mL
  • Volume = 205 mL
Then multiply: \( \text{Mass} = 0.798 \times 205 = 163.59 \).

This calculation shows that the mass of ethanol in this volume is 163.59 grams. Calculating mass this way is very straightforward once you have density and volume.
Ethanol Properties
Ethanol, commonly referred to as grain alcohol, is a versatile chemical compound that appears as a colorless liquid. It's significant for various uses, including serving as an ingredient in alcoholic beverages, a solvent in laboratories, and even as a fuel additive.

One of the key properties of ethanol is its density. At room temperature, the density of ethanol is typically about 0.798 g/mL. This is slightly less than the density of water, which means ethanol floats on water.
  • Being less dense than water affects its behavior in mixtures and solutions.
  • Ethanol is highly flammable, which is important when handling it in various applications.
  • It is miscible with water, making it useful for mixing and producing solutions.
Understanding these characteristics helps in working safely with ethanol and utilizing its properties effectively in different situations.
Volume Calculation
Calculating volume is essential in applications where you need to determine how much space a substance occupies. In scenarios where mass and density are known, you can calculate the volume using the formula rearranged from the mass formula: \( \text{Volume} = \frac{\text{Mass}}{\text{Density}} \).

Usually, when dealing with liquids like ethanol, volume is measured in milliliters or liters. If you know the mass and density:
  • Mass = 163.59 g
  • Density = 0.798 g/mL
Use the formula to find the volume:
\( \text{Volume} = \frac{163.59}{0.798} \).

This calculation results in approximately 205 mL, confirming that the ordered mass corresponds to the expected volume. Volume calculations help verify measurements and ensure accurate chemical operations and procedures.

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Most popular questions from this chapter

Name the SI base units that are important in chemistry, and give the SI units for expressing the following: (a) length, (b) volume, (c) mass, (d) time, (e) temperature.

The medicinal thermometer commonly used in homes can be read to \(\pm 0.1^{\circ} \mathrm{F}\), whereas those in the doctor's office may be accurate to \(\pm 0.1^{\circ} \mathrm{C}\). Percent error is often expressed as the absolute value of the difference between the true value and the experimental value, divided by the true value: percent error \(=\frac{\mid \text { true value }-\text { experimental value } \mid}{\text { true value }} \times 100 \%\) The vertical lines indicate absolute value. In degrees Celsius, express the percent error expected from each of these thermometers in measuring a person's body temperature of \(38.9^{\circ} \mathrm{C}\).

Venus, the second closest planet to the sun, has a surface temperature of \(7.3 \times 10^{2} \mathrm{~K}\). Convert this temperature to degrees Celsius and degrees Fahrenheit.

Classify each of the following as an element, a compound, a homogeneous mixture, or a heterogeneous mixture: (a) seawater, (b) helium gas, (c) sodium chloride (salt), (d) a bottle of soft drink, (e) a milkshake, (f) air in a bottle, \((\mathrm{g})\) concrete.

Fluoridation is the process of adding fluorine compounds to drinking water to help fight tooth decay. A concentration of 1 ppm of fluorine is sufficient for the purpose ( 1 ppm means one part per million, or \(1 \mathrm{~g}\) of fluorine per 1 million g of water). The compound normally chosen for fluoridation is sodium fluoride, which is also added to some toothpastes. Calculate the quantity of sodium fluoride in kilograms needed per year for a city of 50,000 people if the daily consumption of water per person is 150 gal. What percent of the sodium fluoride is "wasted" if each person uses only 6.0 \(\mathrm{L}\) of water a day for drinking and cooking (sodium fluoride is 45.0 percent fluorine by mass; \(1 \mathrm{gal}=3.79 \mathrm{~L} ;\) 1 year \(=365\) days; 1 ton \(=2000 \mathrm{lb} ; 1 \mathrm{lb}=453.6 \mathrm{~g}\); density of water \(=1.0 \mathrm{~g} / \mathrm{mL}\) )?
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