One mole of hydrogen gas (molar mass = 2.0 g/mol)has an rms velocity of 2.0 $\times$ 10³ m/s.To what temperature on the Celsius scale does this correspond?

Question

Quizplus · Accepted Answer

The root mean square (rms) velocity of a gas is given by the formula $v_{rms} = \sqrt{\frac{3kT}{m}}$, where $k$ is the Boltzmann constant, $T$ is the temperature in Kelvin, and $m$ is the mass of one molecule of the gas. To find the temperature in Celsius, we first need to solve for $T$ in Kelvin and then convert to Celsius. Given the rms velocity and the molar mass of hydrogen, we can rearrange the formula to solve for $T$, and after calculating, we find that the temperature that corresponds to the given rms velocity is closest to 48°C, considering the conversion from Kelvin to Celsius ($°C = K - 273.15$).

One Mole of Hydrogen Gas (Molar Mass = 2 ×\times× 103 M/s

One Mole of Hydrogen Gas (Molar Mass = 2 $\times$ 10³ M/s