Speed Distribution of N2 Molecules at 280 K

What is the speed distribution of N2 molecules at 280 K?

Calculate the fraction of N2 molecules that have speeds in the range 260 to 270 m/s.

Answer:

To calculate the fraction of N2 molecules that have speeds in the range of 260 to 270 m/s, we can use the Maxwell-Boltzmann speed distribution equation.

The Maxwell-Boltzmann speed distribution equation is represented as: f(v) = (4πN / (RT))^0.5 * v^2 * exp(-mv^2 / (2RT)) Where: f(v) is the fraction of molecules with speed v N is the total number of molecules R is the gas constant (8.314 J/(mol*K)) T is the temperature in Kelvin m is the molar mass of N2 (28 g/mol) First, we need to convert the given temperature from Kelvin to Celsius: T_Celsius = 280 K - 273.15 = 6.85°C Without the total number of molecules (N) provided in the question, we cannot directly calculate the fraction of N2 molecules that have speeds in the specified range. If the value of N is provided, we can proceed with the calculation using the given temperature and speed range.