What is the speed of air molecules in a 50 degrees celsius room?

Answer 1

Not enough info. You need mass. Here is the formula.

Velocity(root mean square) = sqrt(3*gas constant(R) *temp in Kelvin(K)/mass) Two equations should be used:

p = 1/3 d<c2> ------1

where

p is pressure

d is density

and <c2> is mean square speed.

pV = nRT ------2

where

p is pressure

V is volume

n is number of moles of gas

R is the molar gas constant

and T is the thermodynamic temperature

From 1:

p = 1/3 Mr/VM <c2>

where density has been replaced by molar mass Mr divided by molar volume VM

Thus, pVM = 1/3 Mr <c2>

From 2:

pVM = RT (n = 1)

Therefore:

RT = 1/3 Mr <c2>

(<c2>)1/2 = (3RT/Mr)1/2 ------3

R = 8.314 JK-1mol-1

For air at a temperature of 50oC,

T = 273 +50 = 323 K

Mr = 0.8(28) + 0.2(32) = 28.8 g = 0.0288 kg

(Nitrogen has an approximate abundance of 80 % and molar mass 28 g and oxygen has an approximate abundance of 20% and molar mass 32 g)

Plugging in the values in the above equation 3, the speed of air molecules can be found. It is 529 ms-1.

This is a very large value. We might think that the molecules do not travel at these high speeds, but, in fact, they do. We can only be aware of the pressure they exert.(atmospheric pressure)