Question

Using a numerical integration method such as Simpson’s rule, find the fraction of molecules in a sample of oxygen gas at a temperature of 250 K that have speeds between 100 m/s and 150 m/s. The molar mass of oxygen (O2) is 32.0 g/mol. A precision to two significant digits is enough.

a) 0.15
b) 0.20
c) 0.25
d) 0.30

Answer 1

To find the fraction of molecules with speeds between 100 m/s and 150 m/s in a sample of oxygen gas at a temperature of 250 K, we can use Simpson’s rule to perform numerical integration.

Step-by-step explanation:

To find the fraction of molecules with speeds between 100 m/s and 150 m/s in a sample of oxygen gas at a temperature of 250 K, we can use Simpson’s rule to perform numerical integration.

The fraction can be calculated using the formula:

Fraction = (∫[100, 150] N(v)dv) / N_total

where N(v) is the speed distribution function and N_total is the total number of molecules. The speed distribution function for oxygen gas at 250 K can be obtained from the Maxwell-Boltzmann speed distribution equation.