Question

Find the values of the root mean square translational speed v, molecules in gaseous diatomic oxygen (O2), gaseous carbon dioxide (CO2), and gaseous diatomic hydrogen (H2), at temperature 100° C.

Answer 1

Answer:

For diatomic oxygen:V=539.06 m/s

For carbon dia oxide:V=459.71 m/s

For dia atomic hydrogen:V=2156.25 m/s

Explanation:

As we know that

Root mean square velocity V

$V=\sqrt{\dfrac{3RT}{M}}$

Where

R is the gas constant

$R=8.31\ \frac{kg.m^2}{s^2.mol.K}$

T is the temperature (K).

M is the molecular weight.

For diatomic oxygen:

M=32 g/mol

T=273+100 = 373 K

$R=8.31\ \frac{kg.m^2}{s^2.mol.K}$

$V=\sqrt{\dfrac{3RT}{M}}$

$V=\sqrt{\dfrac{3\times 8.31\times 373}{32\times 10^{-3}}}$

V=539.06 m/s

For carbon dia oxide

M=44 g/mol

T=273+100 = 373 K

$R=8.31\ \frac{kg.m^2}{s^2.mol.K}$

$V=\sqrt{\dfrac{3RT}{M}}$

$V=\sqrt{\dfrac{3\times 8.31\times 373}{44\times 10^{-3}}}$

V=459.71 m/s

For dia atomic hydrogen:

M= 2 g/mol

T=273+100 = 373 K

$R=8.31\ \frac{kg.m^2}{s^2.mol.K}$

$V=\sqrt{\dfrac{3RT}{M}}$

$V=\sqrt{\dfrac{3\times 8.31\times 373}{2\times 10^{-3}}}$

V=2156.25 m/s