Final answer:
The root mean square speed of a N2 molecule at 25 °C is approximately 1.1 km/s.
Step-by-step explanation:
The root mean square speed of a gas molecule is directly proportional to the square root of its temperature. Therefore, we can use this proportionality to find the root mean square speed of a N2 molecule at 25 °C.
Since the root mean square speed of H2 molecules at 25 °C is given as 1.6 km/s, we can use the formula v = sqrt(3RT/M), where R is the gas constant, T is the temperature in Kelvin, and M is the molar mass. The molar mass of N2 is 28 g/mol. By substituting the known values into the formula, we can solve for v, which gives us the root mean square speed of the N2 molecule.
Thus, the root mean square speed of a N2 molecule at 25 °C is approximately 1.1 km/s.