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Mercury is the only metal that is a liquid at room temperature. Its density is \(13.6 \mathrm{~g} / \mathrm{mL} .\) How many grams of mercury will occupy a volume of \(95.8 \mathrm{~mL} ?\)

Short Answer

Expert verified
The mass of mercury is 1302.88 grams.

Step by step solution

01

Write Down Known Values

Identify the known values from the problem. Here, we know the density of mercury, \(\rho = 13.6 \text{ g/mL}\), and the volume of mercury, \(V = 95.8 \text{ mL}\).
02

Use the Density Formula

Recall the density formula, which states \(\text{Density} = \frac{\text{Mass}}{\text{Volume}}\). Rearrange the formula to solve for mass, \(\text{Mass} = \text{Density} \times \text{Volume}\).
03

Calculate the Mass of Mercury

Substitute the known values into the rearranged formula: \(\text{Mass} = 13.6 \text{ g/mL} \times 95.8 \text{ mL}\). When we perform the multiplication, we get \(\text{Mass} = 1302.88 \text{ g}\).

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Key Concepts

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

Mercury Properties
Mercury is a unique metal, most notably because it is a liquid at room temperature. This is rather unusual for metals, as they are typically solid under such conditions. Mercury is represented by the symbol Hg in the periodic table and has many fascinating properties.
Its density is one of its most significant characteristics. With a density of 13.6 grams per milliliter (g/mL), mercury is much denser than water, which has a density of about 1 g/mL. This high density is one reason why mercury is used in devices like barometers and thermometers, as it can accurately gauge pressure changes.
Moreover, the metal is shiny and silvery, making it visually striking. These properties make mercury quite distinct from other elements, and understanding its density is crucial when working with it.
Density Formula
The density formula is a fundamental concept in science that helps us understand how mass and volume relate to each other. It is expressed as:
\[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \]
This formula reveals the mass per unit volume of a substance. In practical terms, density tells us how much material exists in a given space, which is crucial for understanding and predicting the behavior of materials in different contexts.
To find a substance's mass using its density and volume, we can rearrange the formula to:
\[ \text{Mass} = \text{Density} \times \text{Volume} \]
This version helps calculate how much mass is present in a specific volume of a substance, which is useful in various calculations and real-world applications.
Mass Calculation
Mass calculation is essential for determining how much matter is present in an object or substance. To calculate the mass, especially for liquids like mercury, we use the rearranged density formula:
\[ \text{Mass} = \text{Density} \times \text{Volume} \]
In our example, mercury’s density is 13.6 g/mL, and we're given a volume of 95.8 mL. By substituting these values into the formula, we calculate:
\[ \text{Mass} = 13.6 \text{ g/mL} \times 95.8 \text{ mL} = 1302.88 \text{ g} \]
This result tells us that 95.8 mL of mercury would have a mass of 1302.88 grams. Knowing how to perform this calculation is critical for scientific experiments and industrial processes where precise measurements are required.
Volume and Mass Relationship
Understanding the volume and mass relationship is key in various scientific and engineering applications. The relationship is straightforward: given the density of a material, the volume directly influences the mass. For a constant density, if the volume increases, the mass also increases proportionally.
The formula involving density makes this relationship clear, showing that mass is the product of density and volume. This means that if you know any two of these variables, you can always find the third.
In practice, this relationship is incredibly useful. For example, in chemistry, knowing the volume of a liquid and understanding its density allows you to calculate its mass, which is vital for mixing and reacting chemical substances accurately. Furthermore, industries dealing with fluid dynamics rely heavily on understanding how changes in volume affect mass for designing efficient systems.
By mastering these concepts, we gain insights into how materials behave and how to manipulate them for desired outcomes.

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Most popular questions from this chapter

Suppose that a new temperature scale has been devised on which the melting point of ethanol \(\left(-117.3^{\circ} \mathrm{C}\right)\) and the boiling point of ethanol \(\left(78.3^{\circ} \mathrm{C}\right)\) are taken as \(0^{\circ} \mathrm{S}\) and \(100^{\circ} \mathrm{S},\) respectively, where \(\mathrm{S}\) is the symbol for the new temperature scale. Derive an equation relating a reading on this scale to a reading on the Celsius scale. What would this thermometer read at \(25^{\circ} \mathrm{C} ?\)

Write the numbers for these prefixes: (a) mega-, (b) kilo-, (c) deci-, (d) centi-, (e) milli-, (f) micro-, (g) nano-, (h) pico-.

One gallon of gasoline burned in an automobile's engine produces on the average \(9.5 \mathrm{~kg}\) of carbon dioxide, which is a greenhouse gas, that is, it promotes the warming of Earth's atmosphere. Calculate the annual production of carbon dioxide in kilograms if there are 40 million cars in the United States, and each car covers a distance of \(5000 \mathrm{mi}\) at a consumption rate of 20 mi per gallon.

The thin outer layer of Earth, called the crust, contains only 0.50 percent of Earth's total mass and yet is the source of almost all the elements (the atmosphere provides elements such as oxygen, nitrogen, and a few other gases). Silicon (Si) is the second most abundant element in Earth's crust ( 27.2 percent by mass). Calculate the mass of silicon in kilograms in Earth's crust. (The mass of Earth is \(5.9 \times 10^{21}\) tons. 1 ton \(=2000 \mathrm{lb} ; 1 \mathrm{lb}=453.6 \mathrm{~g} .)\)

Which of these statements is scientifically correct? "The mass of the student is \(56 \mathrm{~kg}\)." "The weight of the student is \(56 \mathrm{~kg}\)."

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