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Chapter 1: Problem 16

Iron pyrite is often called "fool's gold" because it looks like gold (see page 19 ). Suppose you have a solid that looks like gold, but you believe it to be fool's gold. The sample has a mass of \(23.5 \mathrm{g} .\) When the sample is lowered into the water in a graduated cylinder (see Study Question 15 ), the water level rises from \(47.5 \mathrm{mL}\) to \(52.2 \mathrm{mL}\). Is the sample fool's gold \(\left(d=5.00 \mathrm{g} / \mathrm{cm}^{3}\right)\) or "real" gold \(\left(d=19.3 \mathrm{g} / \mathrm{cm}^{3}\right) ?\)

Short Answer

Expert verified
The sample is likely fool's gold, as its density is approximately 5.00 g/cm鲁.

Step by step solution

01

Determine the Volume of the Solid

The volume of the solid can be calculated by subtracting the initial water level from the final water level in the graduated cylinder. Given that the initial water level is 47.5 mL and the final water level is 52.2 mL, the volume of the solid is \(52.2 \, \mathrm{mL} - 47.5 \, \mathrm{mL} = 4.7 \, \mathrm{mL}\).
02

Calculate the Density of the Solid

Density is defined as mass divided by volume. Given that the mass of the sample is 23.5 g and the volume is 4.7 mL, the density can be calculated as \( \text{Density} = \frac{23.5 \, \mathrm{g}}{4.7 \, \mathrm{mL}} \approx 5.00 \, \mathrm{g/cm}^3\).
03

Compare the Density to Known Values

Compare the calculated density of the solid with the densities of iron pyrite and gold. The density of iron pyrite is \(5.00 \, \mathrm{g/cm}^3\) and the density of gold is \(19.3 \, \mathrm{g/cm}^3\). Since the calculated density matches the density of iron pyrite, the sample is likely iron pyrite, also known as "fool's gold."

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Key Concepts

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

Density Calculation
Understanding the concept of density is crucial in identifying substances based on their mass and volume. Density is a measure of how much mass is contained in a given unit of volume. It is expressed mathematically as:
  • \( \text{Density} = \frac{\text{Mass}}{\text{Volume}} \)
In our example, the mass of the sample is given as \(23.5 \, \text{g}\) and its volume has been determined to be \(4.7 \, \text{mL}\). By substituting these values into the formula, the density is calculated to be approximately \(5.00 \, \text{g/cm}^3\). This calculation reveals how density can help distinguish between different materials by comparing this result to known density values of other substances.
Volume Measurement
Volume measurement is a vital component in calculating the density of a substance. In our exercise, the volume of the solid was found using water displacement in a graduated cylinder. Here's how it works:
  • First, record the initial water level in the graduated cylinder before the solid is added. In this case, it was \(47.5 \, \text{mL}\).
  • Then, gently lower the solid into the cylinder and note the new water level, which was \(52.2 \, \text{mL}\) here.
  • The volume of the solid is simply the difference between these two levels: \(52.2 \, \text{mL} - 47.5 \, \text{mL} = 4.7 \, \text{mL}\).
This method works because the volume of water displaced by the solid is equal to the volume of the solid itself, assuming no water is spilled out due to the immersion.
Material Identification
Once the density of a sample is known, it can be compared to the known densities of various materials to identify what the sample is likely to be. This is an essential step in distinguishing substances that may appear similar in appearance.
  • For example, gold has a density of \(19.3 \, \text{g/cm}^3\), which is notably higher than that of iron pyrite, \(5.00 \, \text{g/cm}^3\).
  • In our scenario, the calculated density of the sample was approximately \(5.00 \, \text{g/cm}^3\), perfectly matching the density of iron pyrite, commonly known as "fool's gold."
By using density values, one can make informed conclusions about the composition of a material, even when they are visually deceiving.

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Most popular questions from this chapter

The following photo shows the element potassium reacting with water to form the element hydrogen, a gas, and a solution of the compound potassium hydroxide. (IMAGE CAN'T COPY) (a) What states of matter are involved in the reaction? (b) Is the observed change chemical or physical? (c) What are the reactants in this reaction and what are the products? (d) What qualitative observations can be made concerning this reaction?

To determine the average mass of a popcorn kernel you collect the following data: $$\begin{array}{ll} \hline \text { Number of kernels } & \text { Mass }(\mathrm{g}) \\ \hline 5 & 0.836 \\ 12 & 2.162 \\ 35 & 5.801 \\ \hline \end{array}$$ Plot the data with number of kernels on the \(x\) -axis and mass on the y-axis. Draw the best straight line using the points on the graph (or do a least- squares or linear regression analysis using a computer program) and then write the equation for the resulting straight line. What is the slope of the line? What does the slope of the line signify about the mass of a popcorn kernel? What is the mass of 50 popcorn kernels? How many kernels are there in a handful of popcorn \((20.88 \mathrm{g}) ?\)

Express the following numbers in fixed notation (e.g., \(\left.123 \times 10^{2}=123\right)\) (a) \(1.62 \times 10^{3}\) (b) \(2.57 \times 10^{-4}\) (c) \(6.32 \times 10^{-2}\)

Solve the following equation for the unknown value, \(n\) $$ (2.34)(15.6)=n(0.0821)(273) $$

Milk in a glass bottle was placed in the freezer compartment of a refrigerator overnight. By morning a column of frozen milk emerged from the bottle. Explain this observation.(IMAGE CAN'T COPY)
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