Question

at what temperature is the rms speed of hydrogen molecules, which have a molecular weight of equal to

Answer 1

The temperature at which the RMS speed of hydrogen molecules, with a molecular mass of 2.016 g/mol, is equal to the given value can be calculated using the equation K = 1/2 mv^2 = 3/2 kT.

Step-by-step explanation:

The root-mean-square (RMS) speed of hydrogen molecules can be obtained using the equation: K = 1/2 mv2 = 3/2 kT, where m is the molecular mass, v is the RMS speed, k is the Boltzmann constant, and T is the temperature in Kelvin.

Plugging in the given values, we have 1/2 (2.016 g/mol) (VRMS)2 = (3/2) (1.38 x 10-23 J/K) T.

Simplifying the equation, we can solve for T as follows:

T = (1/3) (VRMS)2 (1.66 x 103 K).

Therefore, the temperature is (1/3) (193 m/s)2 (1.66 x 103 K) ≈ 7.48 x 105 K.

Answer 2

The temperature at which the RMS speed of hydrogen molecules is 193 m/s is approximately 5.06 × 10⁴ Kelvin.

Step-by-step explanation:

The root-mean-square (RMS) speed of hydrogen molecules can be calculated using the formula:

VRMS = √(3kT/m)

where VRMS is the RMS speed, k is the Boltzmann constant (1.38 × 10⁻²³ J/K), T is the temperature in Kelvin, and m is the molecular weight in kg.

Given that the molar mass of hydrogen is equal to 2.016 g/mol, which is equal to 2.016 × 10⁻³ kg/mol, and the given VRMS of 193 m/s, we can solve the equation to find the temperature:

T = (VRMS² × m) / (3k)

Substituting the values, we get:

T = (1932 × 2.016 × 10⁻³) / (3 × 1.38 × 10⁻²³)

T = 5.06 × 10⁴ Kelvin

Therefore, the temperature at which the RMS speed of hydrogen molecules is 193 m/s is approximately 5.06 × 10⁴ Kelvin.