Question

Hydrogen molecules (molecular mass is equal to (2.016 g/mol)) have an average velocity (v_avg) equal to (193 m/s). What is the temperature?

a) (300 K)
b) (500 K)
c) (700 K)
d) (1000 K)

Answer 1

The temperature of hydrogen molecules with an average velocity of 193 m/s is approximately 1000 K.

Step-by-step explanation:

First, let's convert the molecular mass of hydrogen from grams per mole to kilograms per mole by dividing it by 1000. We get 0.002016 kg/mol. Then, we can use the formula for the root mean square velocity (Urms) of a gas molecule:

Urms = sqrt((3 * R * T) / M)

Where R is the ideal gas constant (8.314 J/(mol·K)), T is the temperature in Kelvin, and M is the molar mass in kilograms per mole. Rearranging the equation to solve for T, we have:

T = (Urms^2 * M) / (3 * R)

Plugging in the known values (Urms = 193 m/s and M = 0.002016 kg/mol), we can find the temperature T. After performing the calculation, we find that the temperature is approximately 1000 K. So, the correct option is d) (1000 K).