Achieve Question 17

[dinashirazi4O]

The average speed of a diatomic chlorine molecule at 25 ∘C is 323.9 m⋅s−1 . What is the average wavelength of a chlorine molecule at this temperature? Assume that the molecule acts as a single particle.

I am confused about how to approach this problem. Because it says diatomic for the mass do we double the mass of chlorine? Also I saw that we have to use Avogadro's number but how do we just know that?

[Erika Patel 3I]

Hi, since this is a diatomic atom, you would double the atomic mass. Then you would need to convert to kg/mol (dividing grams by 1000 to get to kilograms). However, this is for 1 mol of chlorine molecules and we are being asked to find the wavelength for a single molecule. Since the conversion is 6.022x10^23 molecules/mol (Avogadro's number) we would divide the mass in kg by Avogadro's number. Then, you would plug this mass along with the given speed into the equation and solve for wavelength.

As to the second part of your question about just "knowing" to use Avogadro's number, I am not sure how to answer that but maybe someone else can.

I hope the steps above help you to solve!

[305954124]

You would start by using the equation lambda=h/mv where we use Planck's constant, the mass of hydrogen by dividing its molar mass by Avogadro's numbers, and the given speed. With this equation, you can calculate the wavelength of a hydrogen molecule.