Multiple Choice
Which of the following best describes how the density of a gas changes as temperature increases, assuming pressure remains constant?
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1. Intro to General Chemistry
Density of Geometric Objects
Multiple Choice
If a cube has sides of 3 nm and a mass of 81 ng, what is its density in g/cm^3?
A
10 g/cm^3
B
0.01 g/cm^3
C
0.1 g/cm^3
D
1.0 g/cm^3
Verified step by step guidance1
Convert the side length of the cube from nanometers (nm) to centimeters (cm). Since 1 nm = 1 \(\times\) 10^{-7} cm, multiply 3 nm by this conversion factor: \(3 \ \text{nm} \times 1 \times 10^{-7} \ \text{cm/nm}\).
Calculate the volume of the cube using the formula for the volume of a cube: \(V = s^3\), where \(s\) is the side length in centimeters. Use the converted side length from step 1.
Convert the mass from nanograms (ng) to grams (g). Since 1 ng = 1 \(\times\) 10^{-9} g, multiply 81 ng by this conversion factor: \(81 \ \text{ng} \times 1 \times 10^{-9} \ \text{g/ng}\).
Calculate the density using the formula \(\rho = \frac{m}{V}\), where \(m\) is the mass in grams and \(V\) is the volume in cubic centimeters.
Compare the calculated density value to the given options to identify the correct answer.
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