At what temperature is the rms speed of hydrogen molecules,H₂,which have a molecular weight of 2.02 g/mole,equal to 2.0 km/s? The Boltzmann constant is 1.38 × 10^-23 J/K and N_A = 6.022 × 10²³ molecules/mol. A)17°C B)34°C C)51°C D)68°C E)72°C

Question

Quizplus · Accepted Answer

To solve this problem, we can use the equation for the root-mean-square speed of gas molecules:

v(rms) = √(3kT/m)

where v(rms) is the root-mean-square speed, k is the Boltzmann constant, T is the temperature in Kelvin, and m is the molecular weight of the gas.

Rearranging this equation, we get:

T = (m * v(rms)^2) / (3k)

Plugging in the given values, we get:

T = (2.02 g/mol * (2000 m/s)^2) / (3 * 1.38 x 10^-23 J/K)

Note that we convert the given speed from km/s to m/s.

Simplifying this expression, we get:

T ≈ 51°C

Therefore, the answer is choice C.

At What Temperature Is the Rms Speed of Hydrogen Molecules,H2,which

At What Temperature Is the Rms Speed of Hydrogen Molecules,H₂,which