Textbook Question
What is the density (g/mL) of each of the following samples?
a. An ebony carving has a mass of 275 g and a volume of 207 cm3.
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1. Matter and Measurements
Density
2:07 minutesProblem 103b
Textbook Question
Today, thermometers containing mercury are used less frequently than in the past because of concerns regarding the toxicity of mercury and because of its relatively high melting point (-39 °C). This means that mercury thermometers cannot be used in very cold environments because the mercury is a solid under such conditions. Alcohol thermometers, however, can be used over a temperature range from -115 °C (the melting point of alcohol) to 78.5 °C (the boiling point of alcohol).
b. The densities of alcohol and mercury are 0.79 g/mL and 13.6 g/mL, respectively. If the volume of liquid in a typical laboratory thermometer is 1.0 mL, what mass of alcohol is contained in the thermometer? What mass of mercury?
Verified step by step guidance1
Step 1: Recall the formula for density, which is given by \( \text{Density} = \frac{\text{Mass}}{\text{Volume}} \). Rearrange this formula to solve for mass: \( \text{Mass} = \text{Density} \times \text{Volume} \).
Step 2: Identify the given values for alcohol. The density of alcohol is 0.79 g/mL, and the volume of liquid in the thermometer is 1.0 mL. Substitute these values into the formula for mass: \( \text{Mass}_{\text{alcohol}} = 0.79 \, \text{g/mL} \times 1.0 \, \text{mL} \).
Step 3: Identify the given values for mercury. The density of mercury is 13.6 g/mL, and the volume of liquid in the thermometer is also 1.0 mL. Substitute these values into the formula for mass: \( \text{Mass}_{\text{mercury}} = 13.6 \, \text{g/mL} \times 1.0 \, \text{mL} \).
Step 4: Perform the multiplication for each case to calculate the mass of alcohol and the mass of mercury. Ensure that the units of mL cancel out, leaving the result in grams (g).
Step 5: Compare the masses of alcohol and mercury to understand the significant difference in their densities and how it affects the mass of liquid in the thermometer.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Density
Density is defined as mass per unit volume, typically expressed in grams per milliliter (g/mL). It is a crucial property that helps determine how much mass a substance has in a given volume. For example, if a liquid has a density of 0.79 g/mL, this means that 1 mL of that liquid weighs 0.79 grams. Understanding density is essential for calculating the mass of liquids in thermometers.
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Thermal Properties of Liquids
Thermal properties of liquids, such as melting and boiling points, dictate their behavior under varying temperature conditions. For instance, mercury has a melting point of -39°C, making it unsuitable for very cold environments, while alcohol remains liquid down to -115°C. These properties are vital for selecting appropriate liquids for thermometers based on the temperature range they will measure.
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Mass Calculation
Mass calculation involves using the formula mass = density × volume to determine the mass of a substance when its density and volume are known. In the context of the question, this formula allows us to calculate the mass of both alcohol and mercury in a thermometer by applying their respective densities to the given volume of 1.0 mL.
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