The molecular weight of carbon dioxide is 44.0 g/mol. What is the internal energy in 3.00 kg of carbon dioxide at 300 K? As an approximation, treat the carbon dioxide gas as if it was monatomic.

Question

Quizplus · Accepted Answer

The internal energy of a monatomic gas can be calculated using the formula:

U = (3/2)NkT

where
U = internal energy
N = number of particles (in this case, we can use Avogadro's number to convert from mass to number of particles)
k = Boltzmann's constant
T = temperature

First, we need to calculate the number of particles in 3.00 kg of carbon dioxide:

n = (3.00 kg) / (44.0 g/mol) * (1 mol / 6.022 * 10^23 particles) = 1.70 * 10^25 particles

Then, we can plug in the values into the formula:

U = (3/2) * (1.70 * 10^25) * (1.38 * 10^-23 J/K) * (300 K) = 2.55 * 10^14 J

Using scientific notation, the answer is 2.55 × 10^14 J, which corresponds to choice A.

The Molecular Weight of Carbon Dioxide Is 44