At what temperature do the molecules of nitrogen gas have an rms speed of 35 ?

For the given rms speed of 35 (m/s)

You can determine the temperature from the relation:
(rms speed)² = 3RT/molar mass, or
Temperature, T = (rms speed)²*(molar mass)/(3R)
R=gas constant, 8.31 J/°K-mol
T=temperature in °K
molar mass = kg/mol

T=(35² m²/s²)*(0.028 kg/mol)/(3*8.31 kg-m²/°K-mol-s²)
=35²*0.028/(3*8.31) °K
=1.38 °K

I do not know if the equation still holds at such low temperatures.

The root mean square (rms) speed of gas molecules can be determined using the formula:

vrms = sqrt((3 * k * T) / m),

where vrms is the rms speed, k is the Boltzmann constant (1.38 x 10^-23 J/K), T is the temperature in Kelvin, and m is the molar mass of the gas.

For nitrogen gas (N2), the molar mass is approximately 28.0134 g/mol.

To find the temperature at which the rms speed of nitrogen gas molecules is 35 m/s, we can rearrange the formula as follows:

T = (vrms^2 * m) / (3 * k).

Plugging in the given values, we get:

T = (35^2 * 0.0280134 kg/mol) / (3 * 1.38 x 10^-23 J/K).

Calculating this equation will give us the temperature.

To find the temperature at which the molecules of nitrogen gas have an rms (root mean square) speed of 35, we can use the formula for rms speed:

v = √(3kT/m)

Where:
v is the rms speed
k is the Boltzmann constant (1.38 × 10^−23 J/K)
T is the temperature in Kelvin
m is the molar mass of the gas (in this case, the molar mass of nitrogen gas is 28.0134 g/mol)

Rearranging the formula, we get:

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

Now, we substitute the given values into the equation:

T = (35^2 * 0.0280134 kg/mol) / (3 * 1.38 × 10^−23 J/K)

First, we need to convert the molar mass of nitrogen gas from grams to kilograms:

m = 0.0280134 kg/mol

Now, we can calculate the temperature:

T = (35^2 * 0.0280134 kg/mol) / (3 * 1.38 × 10^−23 J/K)

T ≈ 17331 K

Therefore, the temperature at which the molecules of nitrogen gas have an rms speed of 35 is approximately 17331 Kelvin.