Question

Calculate the root mean square speed of h2 molecules. Given that density of gas at 3atm is 0.09gm /dm^3

Answer 1

RMS velocity is given by $v_{rms}=\sqrt{\frac{3P}{\rho}}$

here P is the pressure, $\rho$ is the density of gas.

here, P = 3 atm = 3 × 1.013 × 10^5 N/m²
$\rho$=0.09 g/dm³ = 0.09 kg/m³

now, $v_{rms}=\sqrt{\frac{3\times10.13\times10^5}{0.09}}$

= 1837.57 m/s

Answer 2

Answer:

The root mean square speed is 1006.09 m/s.

Explanation:

Pressure of the hydrogen gas,P = 3 atm

Density of the gas = $d= 0.09 g/dm^3=0.09 g/L$

Temperature of the gas = T

Molar mas of hydrogen gas,M = 2 g/mol

$PM=d\times R\times T$

$T=\frac{PM}{dR}=\frac{3 atm\times 2 g/mol}{0.09 g/L\times 0.0821 atm L/mol K}=812.018 K$

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 = 812.018 K

M = atomic mass = 0.02 kg/mole

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

$\nu_{rms}=\sqrt{\frac{3\times (1.38\times 10^{-23}J/K)\times (6.02\times 10^{23}mol^{-1})\times (812.018K)}{0.02kg}}$

$\nu_{rms}=1006.09 m/s$

The root mean square speed is 1006.09 m/s.