Question

1. a common diatomic gas sample weighing 1.561 g fills a balloon to 1.35 L at STP. compute the molar mass of the gas and identify it

2. how many electrons in an atom can have quantum numbers :

a. n=2

b. n=3 and ms=+1/2

c. n=1 and l=1

Answer 1

1.

Assuming the gas obey's ideal gas law

Where m = mass = 1.561 g

M = molar mass of the gas

p = standard pressure = 1 bar

T = standard temperature = 273.15 K

V = Volume = 1.35 L

R = gas constant =

Hence, solving the ideal gas equation we get

The closest diatomic molecule with similar molar mass is with molar mass of 28 g/mol.

Hence, the gas must be nitrogen.

2.

a. for n=2

  The allowed values of l are 0 and 1.

The corresponding orbitals are 2s and three degenerate 2p orbitals.

Hence, total number of electrons that can have n=2 is  

Alternatively, for any shell n, the number of electrons it can hold is given by.

Hence, for n=2

b. for n=3 and m_s = +1/2

Lets calculate the number of electrons with n=3 first.

Now, exactly half of those electrons will have spin up (m_s = +1/2) and other half will have spin down(m_s = -1/2).

Hence, the required number of electrons with quantum numbers n=3 and m_s = +1/2 is

c. n=1 and l =1

  Note that for n=1, the allowed values of l is from 0 to n-1. i.e only possible value of l = 0.

Hence, no electron can have n=1 and l=1.

Hence, 0 electrons can have n=1 and l=1.