Question

Calculate the root mean square velocity of nitrogen molecules at 25°c

Answer 1

check the Attachment

Answer 2

The root mean square velocity of nitrogen molecules at 25°c is 515 m/s

Explanation:

The formula used for root mean square speed is

$\nu_{rms}=\sqrt{\frac{3kN_AT}{M}}$

where,

$\nu_{rms}$  = root mean square speed

k = Boltzmann’s constant = $1.38\times 10^{-23}J/K$

T = temperature = [$25^0C=(25+273)=298K$

M = atomic mass of nitrogen molecule = 28 g/mol

$N_A$ = Avogadro’s number = $6.02\times 10^{23}mol^{-1}$

Now put all the given values in the above root mean square speed formula, we get:

$\nu_{rms}=\sqrt{\frac{3\times (1.38\times 10^{-23}J/K)\times (6.02\times 10^{23}mol^{-1})\times (298K)}{28\times 10^{-3}kg/mol}}$

$\nu_{rms}=515m/s$

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