Nitrous oxide, N2O, has been used as a dental anesthetic. Suppose that the average speed of an N2O molecule at 25°C is 377 m/s. (It is actually 379 m/s.) Calculate the kinetic energy (in joules) of an N2O molecule traveling at this speed.
To calculate the kinetic energy of an N2O molecule traveling at a given speed, we can use the equation for kinetic energy:
Kinetic Energy = (1/2) * mass * velocity^2
In this case, we are given the speed of the N2O molecule, but we need to find the mass of the molecule. To do so, we'll use the molar mass of N2O and the Avogadro's number.
First, we need to determine the molar mass of N2O:
N2O is composed of two nitrogen atoms (N) and one oxygen atom (O).
The atomic masses of nitrogen (N) and oxygen (O) are approximately:
Nitrogen (N) = 14.0067 grams/mol
Oxygen (O) = 15.999 grams/mol
To calculate the molar mass of N2O, we multiply the atomic masses of nitrogen and oxygen by their respective subscripts:
Molar mass of N2O = (2 * atomic mass of N) + atomic mass of O = (2 * 14.0067 g/mol) + 15.999 g/mol
Molar mass of N2O = 44.0128 g/mol (approximately)
Next, we need to convert the molar mass from grams/mol to kilograms per molecule. We do this by using Avogadro's number.
Avogadro's number, NA = 6.022 x 10^23 molecules/mol
Now, we can calculate the mass of one N2O molecule in kilograms:
Mass of one N2O molecule = (molar mass of N2O / Avogadro's number) kg/molecule
Mass of one N2O molecule = (44.0128 g/mol / (6.022 x 10^23 molecules/mol)) kg/molecule
Now that we have the mass of one N2O molecule, we can substitute this value along with the velocity into the kinetic energy equation:
Kinetic Energy = (1/2) * mass * velocity^2
Substituting the values:
Kinetic Energy = (1/2) * (mass of one N2O molecule) * (velocity)^2
Now we can plug in the values and calculate the kinetic energy.