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Chromium crystallizes in a body-centered cubic structure with an atomic radius of 125 pm. Given that the atomic mass of chromium is 51.9961 g/mol, estimate the density of Cr metal in g/cm³.
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1. Intro to General Chemistry
Density of Geometric Objects
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Which of the following best describes how the density of a gas changes as temperature increases, assuming pressure remains constant?
A
The density of the gas decreases.
B
The density of the gas remains unchanged.
C
The density of the gas increases.
D
The density of the gas first increases, then decreases.
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Recall the ideal gas law: \(P V = n R T\), where \(P\) is pressure, \(V\) is volume, \(n\) is moles of gas, \(R\) is the gas constant, and \(T\) is temperature in Kelvin.
Since pressure \(P\) is constant, rearrange the ideal gas law to express volume \(V\) as a function of temperature: \(V = \frac{n R T}{P}\).
Understand that density \(\rho\) is defined as mass divided by volume: \(\rho = \frac{m}{V}\). For a given amount of gas, mass \(m\) is constant.
As temperature \(T\) increases, volume \(V\) increases proportionally (from step 2), so the denominator in the density expression increases, causing density \(\rho\) to decrease.
Therefore, under constant pressure, the density of a gas decreases as temperature increases.
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