Question

Suppose that the root‑mean‑square velocity vrms of carbon dioxide molecules (molecular mass is equal to 44.0 g/mol ) in a flame is found to be 1310 m/s. What temperature T does this represent? The Boltzmann constant is k=1.38×10−23 J/K and Avogadro's number is ????A=6.022×1023 mol−1.

Answer 1

Answer : The value of temperature is, 3028.7 K

Explanation :

The formula used for root mean square speed is:

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

where,

$\nu_{rms}$ = root mean square speed  = 1310 m/s

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

T = temperature = ?

M = molar mass = 44.0 g/mole  = 0.044 kg/mol

$N_A$ = Avogadro’s number = $6.022\times 10^{23}mol^{-1}$

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

$1310m/s=\sqrt{\frac{3\times (1.38\times 10^{-23}J/K)\times (6.022\times 10^{23}mol^{-1})\times (T)}{0.044kg/mol}}$

$T=3028.7K$

Therefore, the value of temperature is, 3028.7 K